How can I save the world from the spread of Hallow and Corruption/Crimson?

One way to fight(not totally fix the problem unless you are very devoted) is to use vile/purification powder on hallow/corruption blocks respectively. These powders will turn the blocks into regular blocks, though if you take too long to purify the world it may make no difference

Pre-hardmode, your best bet is probably to limit the 'inconvenience' of Corrupted turf, and latter surgically remove areas of severe risk, before summoning and defeating the Wall of Flesh boss (activating Hardmode and the rapid spread of corruption/Hallow).

What I do is to chop down all trees (and remove any chests sitting on grass) in a corrupted area, and then beat the tar out of any and all grass (and thorns) on any exposed surface. I then brick over the entrances to the Chasm, and sprinkle Purification Powder on exposed Ebonstone (Vile/Purification Powders normalize, Holy/Unholy Waters convert a target to the extremes). What ends up happening is that generally, foot traffic through these 'tame' Corrupt areas tends to get interrupted much less by Corruption beasts (with the exception of the occasional Devourer), as most of the "Eater" creatures tend to have to come from the bottom edge of the screen, and get trapped inside their pits.

At this point, I mainly visit the Chasm for Shadow Orb breaking, and collecting Vile Mushrooms (and ripe Deathweed during Blood Moon, until I get enough seeds for a farm). On each visit, I dust the walls/floors with a stack or two of powder. Eventually, when it looks like most of the surface area in a section is pure, I dig down through the pit wall or chasm floor/ceiling, looking for any remaining ebonstone to nix, or corrupt grass spots to pound out. I flatten the surface to make fighting summoned Eater of Worlds bosses easy.

I advise that if you go about 'removing' Corruption, you take your time and do it before you go Hardmode, so that you don't have to do it all in one long, tedious run to avoid a relapse. Even then, I haven't really played into Hardmode yet, so I can't say how drastically you'll have to revise this strategy when it's triggered.

Generally speaking, there's enough clay or unexposed dirt in most strata of the underground's upper layers that you needn't fear needing to blow up the whole world. Remove corrupted/hallowed grass from as much of the surface (and surface caves/pools) as you can, and you should be fine.

It is not worth trying to remove it in your world. make a new world transfer your stuff and use a world with very little corruption. Then just live there until the corruption spreads. Rinse and repeat.

I downloaded Scooterboot's Metroid Mod. Within it I was able to build a weapon that launches missiles that explode tiles. There's also a few other perks.

It takes forever, but is better than sprinkling magic peter pan powder everywhere.

Blow it all up, save the dirt so that you can craft the landscape at your preference.

Start a new world, and use the Purification Powder on the corruption.

Ever since the 1.2 update, the NPC steampunker (gained by killing a mechanical boss) sells the Clentaminator (for 2 platinum coins).

This used with green solution (25 silver) as the ammo will return anything it hits back to the purity (normal grasslands).

It has a range of about 40 so you can make tunnels every 80 blocks and spray in both directions.

As a cheaper answer to corruption you can always go into "my documents/my games/terraria/players" and copy ALL FILES for one player and go back in and out of the game double your purification powder or bombs (or even money) cheating, yes but makes it a little less frustrating.

Although I would more go for the method of mining either side then bomb the middle and build either a platform or bridge over the top.

Get purification powder from your town Dryad. It depends on how much corruption you have to determine how much purification you will need. As far as I know corruption can't spread through dirt so as long as you spread it along the top of the grass and maybe in some chasms if needed you can slowly get rid of it day by day. Try to get rid of most corruption before hardmode, otherwise Corruptors will come and spread more corruption, basically reversing the whole cause. However, if the corruption has already spread a decent amount through a fairly large cave you are most likely hopeless unless you have a ton of bombs/grenades/dynamite

If you are in late game, I suggest getting the rocket launcher (not the snowman cannon due to its homing) and rocket IV, which is sold for 5 silver each during a solar eclipse, or rocket 2, sold for 2 silver 50 copper during a blood moon, the clentaminator from the steampunker for 2 platinum, and green solution (for clentaminator). DISCLAIMER this is recommended if you are as bent on it as me. If not, then biuld a space city (all the npcs will negate most spawning).

I'm in the process of getting rid of corruption and I find that a mix of powder and explosives work well. However in Hardmode if you want to get your world corrupt free you will need a second player otherwise you're screwed.

I just dig holes on either side of the crimson/corruption. If you have enough time, and a pickaxe good enough, then you could dig to the underworld and prevent the corruption/crimson from spreading in that direction.

It really isn't that big of a deal to be honest. Depending on which mode you are playing, you should be able to beat the game before the percentage of corruption hits 20%. And if you really don't want your world becoming fully corruption/crimson, you can just dig a three block wide tunnel with wooden blocks on either side, around your houses.