Why does Loki look "sick" when he first arrives on Earth?

I definitely noticed that as well. He had prominent circles around his eyes, a sickly yellow color, and his voice was tired and weary. He stumbles when he is leading Hawkeye and the professor away to the Jeeps. When he moves into position into the Jeep's trunk, he practically falls into a sitting position. He has to lean heavily on the Jeep's railings as a support during the car chase. He seemed so very weak and sick, he looked as though he was dying- but he seems to get better. I'm not sure as to the origin of this pitiful state, but I can at least verify that your observation is correct- Loki was definitely weak and sweating when he appears on Earth. Perhaps it had something to do with the flashback of that alien touching the side of his head, but I'm not sure. He does say that he is

"burdened with glorious purpose".

It could be that the journey through space, unprotected and without the aid of the Bifrost was strenuous even for his magic and abilities. He says later:

With the Bifrost gone, how much dark energy did the Allfather have to muster to conjure you here, your precious Earth?

He probably had to pour a lot of himself into his own magic to journey, hence the weakened state upon arrival.

Loki is not sick when he gets to Earth. He is EXHAUSTED. He likely used a significant part of his magical energy and drove himself to exhaustion accessing the Tesseract/Cosmic Cube from the other side, opening a portal and getting himself to Earth.

He is reaching across the Nine Realms to access an alien technology and opening a gateway between two distant locations, an outstanding achievement since he did not have any other power source besides himself. He has to later have Professor Erik Selvig build an entire power plant to house the mechanism to create a larger gateway.

This explains why the Bifrost was such a necessary tool in bridging the Nine Realms. It would leave the Asgardians far too vulnerable to their enemies to travel between realms without it.

It is clear that Loki is obviously fatigued and can barely managed to move once he is placed in the bed of the truck. It is only the Asgardian zeal for combat, his superiority of weapons and his centuries of fighting prowess that allows him to easily defeat the SHIELD agents in the facility in his reduced state. (Being bullet-proof doesn't hurt, either.)

Loki, being a powerful sorcerer decided he would fall from the Bifrost and use his magic to find his way to other worlds among the Nine Realms of the World Tree. He was obviously successful finding not only a place where he could take refuge, but he even found allies in the Chitauri, who were willing to offer him an army in exchange for the opportunity to conquer Earth and steal the Tesseract/Cosmic Cube.

It could be that the strain of the magic taken to get him to Earth took its toll. Yet I can't help but think that the circles under his eyes look a lot like the ones under Clint's (Hawkeye) while he's under the mind control.

SPOILER ABOUT AFTER-CREDITS SCENE!!!!!
He Probably Looks Exhausted/Sick Becauase . . .

Since Thanos is involved, I've often wondered if Loki's stone in his staff/spear is the Mind Gem, one of the Infinity/Soul Gems. Once marvel retconned them from all being "soul gems" (and all green, I think) to being different colored Infinity Gems, the Mind Gem was/is the blue shiny one. Think about it---it's blue, he controls folk's minds with it, he manipulates the Avengers with it on the Hellicarrier (or somehow the gem does when they're all arguing: Dr. Banner, put down the spear!!!

On the Infinity Gems: http://tinyurl.com/lmr64e2 --- http://tinyurl.com/kmqey67

Okay so here's what I'm thinking:
The Gems have an organic relationship. They affect each other. As stated in the first link, and somewhat obvious, the power gem augments the mind gem. It is reasonable to posit that using the mind gem would be taxing for the user without also having the Power Gem as a source. You'll notice Loki is spry for a bit but is taxed again after using the gem/stone/spear (both as a weapon and to control Hawkeye and the Selvig (sp?) )

EDIT: I removed spoiler/hidden text b/c (A) a prior post already includes a pic of Thanos, and (B) Avengers has been out over a year now.

I saw an interesting theory about this actually. He was being tortured. Someone commented on how, as the movie progresses, Loki begins to look stronger and less sickly. Meaning wherever he came from caused his weakened form, a.k.a. Thanos and the Chitari.

They were torturing him to work with them, which I believe fits Loki's personality more than having him help them willingly. It could also explain the "burdened" part of "burdened with glorious purpose".

Later we see Loki being essentially bullied by the Other. He manages to cause Loki physical pain which we see later in the film isn't an easy task. Loki is shot by Coulson, fights Thor (who is obviously much stronger than him), and goes up against the Hulk and the only one who does enough damage to take him out is Hulk.

Personally, I believe this theory over the rest but the only ones who can confirm anything (cast and crew of the film) haven't said anything about it.

He was somewhat under the influence of the Tesseract, similar to Hawkeye and Selvig. Loki is not normally a very great guy, but in the Avengers he was not really himself.

I have seen it written in many places and in the comics that Thanos is one for torture. At the end of Thor, it appears that Loki really just wants to die. However, it is very likely that he was picked up by Thanos and then tortured by him to make him aid Thanos and the Other with the attack on earth due to Loki having access to the Vault on Asgard where the Infinity Gauntlet is kept. Both movies seem to be connected with this. If you look at the after credits scene of Thor, Loki looks like total sh**. His face has been burned severely, his eyes have circles engulfing them and his teeth have rotted greatly. He was obviously burned, which would be a form of torture that Thanos would subdue against a frost giant. Then, in the Avengers, Loki is ill and weak, nearly the whole way through. Many say Tom tripped when leaving SHIELD, but that is incorrect. Loki hunches over in pain as he is leaving, basically falls into the bed of the truck and is seen mostly sitting in the underground tunnels where his team was working. It is also obvious that the Other could inflict pain upon Loki just by touching him. I strongly believe that Loki was tortured by Thanos into helping him get the Tesseract and, eventually, the Gauntlet. Hopefully Marvel will explore it in Thor 3 or the Avengers 3. Fingers crossed that they do because I am really dying to know.

I think he looked sick because... well, if people actually think about it, inside the studio it gets hot fast. 'trust me'. And because of his sweating, he was maybe just really warm. In one of his comments on a different site, it said test jumping in his suit is like jumping while wearing a 40 pound suit. So, hope this helps.

okay i'm thinking, it would be a pretty good "plot twist" if Loki was actually tortured by Thanos. first of all he is very silly and weak, and have dark "spots" under his eyes( much like Clint while he was under mind control) so my theory is that, Thanos tortured him, broke him down, and warped his mind so he could control him. thanos is known for his torture, but the only ones who can truly confirm this are the cast and crew,, but i hope deeply that they would confirm it in avengers or thor 3- personally i think that it would make great depth to Loki,and would make a lot of sense. It would actually explain a lot, anyways hope this helped:)

Hé had the snake poison torture from the myth.

When you see the flashback and before the hand reached his face. You see a snake behind then.

Look up the myth... They worked that into the story with a twist.