Which mob in Minecraft is the best for farming?

Best mob for farming food in game is cows due to them giving steak as well as bonus drops like leather. Cows are manual though. If you want a decent semi-automatic farm, chickens are the way to go. Breeding and loot collection is automatic, you just need to kill them yourselves if you want food.

Best mob for XP is enderman. A farm should only be built in the End. Takes about 1 minute to get from Level 0 to 30 using a farm that is compact but with multiple layers.

Best mob in the overworld for loot is spiders and skeletons. A farm can be built specifically for them if a monster spawner have been found. If not, a multiple layer mob farm (dark room with water channels) will be sufficient.

Depends on what you need it for.

Cows - Leather and Food
Chickens - Feather and Food
Endermen - Pearls
Skeleons - Bones
Spiders - String and potion ingredients
Blazes - Potion ingredients
Wither Skeletons - Wither skulls (but hard to farm without mods)
Zombie Pigmen - Gold

About the only mobs not really worth farming are Zombies (poor food), Creepers (which can destroy your farm), Ghasts (too big and destroy blocks).

Grinding Endermen in the end or grinding Blazes is the best way but if you're too much of a wuss for that, you can always go triple or quad skeleton grinder, fairly easy to build.

Farming for what? XP or food?

The best mob for food is cows as steak is the best food in the game

Breeding chickens I found is the best mob for XP, have a big cage, chickens and a load of seeds and breed away. When you get enough then walk around and keep clicking with the seeds, takes around 3-5 mins to get to level 30.

Like the other person said for food use cows but for xp use blazes go into peaceful mode and build a trap around a blaze spawner water or snowballs work well (fire resistance helps in the nether lol)