What do the Istari in The Lord of the Rings represent?

Tolkien didn't dislike metaphor (his work is full of it), but allegory; it's certainly appropriate to look at what characters represent - but you're unlikely to find a direct parallel with a real person. Note also that the Istari were sent to help Elves and Men, not specifically the Men of Gondor.

Saruman represents the modern world. He gains a significant portion of his power through his speech, which is much more modern than other characters (especially those who are most heroic), and he uses his speech like a modern politician (his rule of the Shire is even fairly Communist). In addition, he makes significant use of technology and machinery - Tolkien was generally opposed to industrialism.

Saruman also plays the role of contrast to both Gandalf and Sauron. He is clearly a lesser copy of Sauron, but he was originally meant (in-universe) for the role that Gandalf assumes. His impatience leads him to first lesser and then greater evil, and his eventual downfall.

Radagast is the opposite of Saruman, in that he is enamoured of nature rather than technology, and peaceful rather than power-hungry. His failure, noted by Tolkien to be lesser than Saruman's (showing Tolkien's preference against the industrial world), is necessary because either extreme must fail - it is the middle ground (represented here by Gandalf) that must succeed. This is the world that (according to Tolkien) could or should have been: a middle ground between nature and machinery.

Radagast fails because his reluctance to act leads him to abandon his mission. Saruman fails because his eagerness to act leads him to evil. Gandalf succeeds because he overcomes his reluctance, and acts only as much as necessary.

The Blue Wizards, Alatar and Pallandro, feature so little in Tolkien's writing that it's difficult to say much about them. In The Peoples of Middle-earth (1968), Tolkien says that their mission was to travel to the east and weaken the forces of Sauron, and that rather than failing, they had a pivotal role in the victories of the West.

But the other two Istari were sent for a different purpose. Morinehtar and Rómestámo. Darkness-slayer and East-helper. Their task was to circumvent Sauron: the bring help to the few tribes of Men that had rebelled from Melkor-worship, to stir up rebellion ... and after his first fall to search out his hiding (in which they failed) and to cause dissension and disarray among the dark East ... They must have had very great influence on the history of the Second Age and Third Age in weakening and disarraying the forces of East ... who would both in the Second Age and Third Age otherwise have ... outnumbered the West.

(Other material in the book points towards their failure - so it seems that Tolkien himself was divided as to their success).

Exactly what happened to them is simply outside of the scope of The Lord of the Rings. Given Tolkien's dislike of allegory, it seems most likely that such minor characters existed primarily to flesh out Arda, rather than directly represent anything/anyone.

The parallel between Gandalf and Christ seems a little coerced and also doesn't really work: Christ did not die to be reborn. Christ died to free man from his sins. Gandalf sacrifices himself, but actually fulfills his mission after and thus despite his sacrifice, whereas Christ fulfills his mission by means of his sacrifice.

Personally, I know too little about Tolkien's stance towards industrialism or communism to support or dispute the interesting interpretations @Tony provided.

The side of Sauron is driven by power hunger, by the will to rule all. They use armies of bread soldiers, who are not only savage, ugly, miserable creatures, but whose sole purpose is to fulfill their masters' mission.
You could see that side as totalitarianism, or even as fascism. The will to establish a total rule and annihilate all that which is different.

The opposite side is basically only defined by not siding with Sauron.

However, initially the opposite side is not actually opposing, even though each and everyone's existence is threatened. It is Gandalf's great achievement to make them oppose, which presupposes their unification.

What he does is to actually shape an opposing side. And the people of this side are not only characterized by the fact, that they are not under the rule of Sauron, but by a common goal. He gives Men back a king. He restores the Elves' willingness to trust Men again. He is the one to orchestrate the alliance of the Free Peoples. He overcomes their reluctance to work together and thereby forges another force of heterogeneous armies, of soldiers who fight for a common cause, which at it's core means everyone's individual freedom and well-being.

At the same time, he does none of this for his own profit. He shows his will to sacrifice himself. He shows the humbleness to ask others for their help.

So while all the Istari set out with a common mission, their achievement greatly differs:

• Radagast is just busying himself with his own interest. He basically excludes himself from the conflict although all that he loves and cares for is in fact at stake.
• The Blue Wizards go fight some individual battles somewhere far away, which may or may not have yielded victories, which - if won - appear to not have much of an importance for the overall war.
• Saruman is seduced and therefore completely loses track of his mission and switches sides. He is corrupted by his power and ego, and by the power of Sauron.
• Gandalf is pragmatic, humble, fiercely determined, open-minded. He always tries to see how the pieces in the conflict are interconnected and therefore often succeeds to move them into the right place. He assumes his responsibility, but he does not throw himself into battle all alone. And he resists temptation.

Gandalf to me represents the willingness to cooperate, in order to actively defend freedom against tyranny.

This is not restricted to historical situations. It is a principle that stands on its own, but is applicable to those situations.
Martin Niemöller once explained the consequences of failing to follow this principle:

In Germany, they came first for the Communists, And I didn’t speak up because I wasn’t a Communist; And then they came for the trade unionists, And I didn’t speak up because I wasn’t a trade unionist; And then they came for the Jews, And I didn’t speak up because I wasn’t a Jew; And then . . . they came for me . . . And by that time there was no one left to speak up.

Gandalf's success is exactly to not let that happen.

You can find a lot of parallels between the attitude of the characters from Tolkien's universe, especially from The Lord of the Rings, with the different parties involved in World War II.

That being said, I don't think that Tolkien intended to (partially or fully) build parallels to any historic events, but rather build a metaphor for general principles, attitudes, ideals or motives, that apply everywhere and therefore also played an important role in specific events.
After all, World War II is the war of a league of tyrants against all other sovereign nations of the world. That being said, there's also a vast part of things, that those two have not in common, most importantly the historical one having the victors slide back into conflict among themselves.
Still, what won both conflicts was the willingness to unite all efforts against "the evil" and overcome all reluctance to work together (which is process that took a long time in both cases).

Gandalf represents that willingness. I suppose that is why he succeeds and the others fail.

I'm a complete newbie fan to the LOTR's, watched the movies when I was younger and hated them but just recently watched them again and fell in love with the whole heroic adventure and amazing story! Now I've been busy studying and getting way deeper into the plot and story.

Anyways, I saw this question and wanted to answer. I'm a christian, and reading on Tolkien's (and Lewis) past helps too but here are some examples you might take into mind. IMO Gandalf IS WIDELY portrayed as a protagonist resembling Christ.

1) As someone stated above, as with Christ, he willing sacrificed himself for Frodo and his friends in the mines and chose death to save them. "No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again...[And] Greater love has no one than this, that one lay down his life for his friends." John 10:18 John 15:13

2) I saw this in a similar question regarding Gandalf, his humanity and angelic nature. After returning from "death" as Gandalf the White, although being in flesh, he states he has forgotten much about his old (fleshly/mortal) existence and remembered much about his forgotten higher "angelic or spiritual" existence... Christ did the same. Though Gandalf was not of human nature, he willingly chose to take on human form and all of its negatives such as aging, fleshly weakness, emotional strain, etc. much as Christ did; I would encourage you to read Hebrews chpt 2 in full before commenting!

Though being of divine nature"Since the children have flesh and blood, he too shared in their humanity so that by his death he might destroy him who holds the power of death—that is, the devil— and free those who all their lives were held in slavery by their fear of death." For this reason he had to be made like his brothers in every way, in order that he might become a merciful and faithful high priest in service to God, and that he might make atonement for the sins of the people. Because he himself suffered when he was tempted, he is able to help those who are being tempted. This says that Christ willing chose to become like man, in order to live with them and ultimately be able understand and emphasize with men and their struggles because he let go of his ultimately divine nature to take a lesser one that he would be able to understand and have compassion on man and their mortal struggles.

Also, Gandalf endured a great battle with the powerful demon in the mine, a ginormous struggle that pushed him and tested his body and strength, physically, spiritually and psychologically. In the end, after a grueling battle, Gandalf was shown to be victorious and ultimately was exalted by Eru by given greater power and a higher position of authority (hence being given the white robes as leader to the wizards). This is much the same as Christ how at the end of his trials and victory through the cross was "exalted by God". Like the battle with the Balrog and the physical trials Gandalf faced, this portrays the struggle of Jesus on earth, as he was subjected to the flesh and temptations of the devil/demons (see 40 day fast and tempting in the desert) and ultimately at Gethsemane on the Cross when he triumphed over Satan and his demons through death (and ultimately his resurrection). Thus when he returns to heaven, God the Father approves of Christ and the trial and suffering he endured to perfect Him and now glorifies Christ and exalts Him higher than ever before.

"In bringing many sons to glory, it was fitting that God, for whom and through whom everything exists, should make the author of their salvation (Jesus) perfect through suffering."Heb2 ....we see him who for a little while was made lower than the angels, namely Jesus, crowned with glory and honor because of the suffering of death, so that by the grace of God he might taste death for everyone.

Thus Jesus is exalted for his sufferings on earth and his heroic valor to save and redeem man. He was not invincible while on earth to succumb to the flesh or pains of mortality; much the same and Gandalf though being of heavenly nature was not removed from the emotional and physical pain of being on earth and in an earthly vessel. Christ and Gandalf were of heavenly origin yet were made, "lower than the angels". In doing so Gandalf relates to man, yet his true nature is not of human nature rather spiritual and heavenly.

And finally THE BIGGEST representation of Gandalf's Christ-like portrayal in the film was his saving entrance at The Battle For Helms Deep. In it, the vast enemy's army, numbering in the thousands, assembles and gathers around the last city and stronghold of those for standing for good and light. just as the enemy surrounds the city and about to overtake it, Gandalf, clothed in shining garments of white, appears above in the sky from the East. As the sun rises, the light shines down from the East onto the west, visible and blinding to the enemies to the West. Then, as if coming down from the sky (heaven) Gandalf and his army (angels) descend from the sky in robes of white and destroy the evil armies to the west with their swords. Here is the bible narrative that backs this account. You'll see the resemblance, just go watch the scene again and how Gandalf is seemingly descending in a blaze of light from the almost heavenly mountain top-position to descend and conquer the enemy army to the West.

For as the lightning comes out of the East, and shines even unto the West, so it will be when the Son of Man comes. (Matt 24:27)

And then at last, the sign that the Son of Man is coming will appear in the heavens....and they will see the Son of Man coming on the clouds of heaven with power and great glory. 31 And he will send out his angels with the mighty blast of a trumpet, and they will gather his chosen ones from all over the world...

(Rev 11) I saw heaven standing open and there before me was a white horse whose rider is called Faithful and True. With justice he judges and makes war. The armies of heaven were following him, riding on white horses and dressed in fine linen, white and clean.

...Out of his mouth comes a sharp sword with which to strike down the nations.

From here, the devil and his armies see the Son of Man (Gandalf) coming down from the sky and they assemble to make war against the rider on the white horse...

Rev:19 Then I saw the Beast and the kings of the earth and their armies gathered together to make war against the rider on the horse (Jesus or Gandalf) and his army. 20But the beast was captured, and with him the false prophet who had performed the miraculous signs on his behalf. With these signs he had deluded those who had received the mark of the beast and worshiped his image. The two of them were thrown alive into the fiery lake of burning sulfur. 21The rest of them were killed with the sword that came out of the mouth of the rider on the horse, and all the birds gorged themselves on their flesh.

And again, in Revelation 20 when satan is loosed, "and he will go out to deceive the nations in the four corners of the earth—Gog and Magog—to gather them for battle. In number they are like the sand on the seashore (much like the orcs in the innumerable army) 9They marched across the breadth of the earth (like the march from middle earth to Helms deep) and surrounded the camp of God’s people (as Gondor in Battle of the Pelennor Fields), the city he loves. But fire came down from heaven and devoured them." Then the devil who deceived them was thrown into the lake of burning sulfur with the beast and the false prophet, and tormented day and night forever and ever.

As you can see, there are MANY similarities with this, especially in the movie. Please watch the scene where Gandalf descends down from the mountain top on his white horse enveloped in light shining from the rising Sun to make war on the orcs to the West. Though the orcs as numerous as the sand on the seashore are surrounding the great city of Gondor where the last forces of good take their stand, Gandalf and his armies (representing Christ and his angels) arrive descending from the heavens and "strike them down with their sharp sword (Rev 19:15).

I saw various other biblical references, especially in the dominance and rise of man though he yet weaker than the other creatures (he is still mortal, fragile and vulnerable with a short lifespan yet still is given great power and dominion over the earth...see Hebrews 2:6-7).

Thanks guys for any comments, please feel free to correct my mistakes or insert correct names/quotations. As I said, I'm just starting to learn about everything and I don't as much as any of you but wanted to share some things I thought were neat and resemblances i caught to biblical prophesy. Hope I could be at least of some little help! Thanks guys for all the exciting questions and explanations! :)