Pickup, Synchronize, Flame Body, Compoundeyes, and Mold Breaker are imo the best ingame abilities. Well, maybe not Mold Breaker overall, but it becomes incredibly useful when you deal with those damn Boldore, as it allows you to bypass Sturdy.
Pickup gives you a 10% chance of picking up an item after battle. I carry around an army of Lillipup until I grab a Pokemon that will be part of my final team. This gives me all the healing items I need, as well as a few Rare Candy if I train them to level 11. This allows you to save your money for some nice stuff (or even make money if you get a Nugget). It also helps out with catching Pokemon early on, as you have a decent chance of getting a Great Ball.
Synchronize makes it so that wild Pokemon you encounter have a 50% chance of being the same nature as the Pokemon with Synchronize. Just grab some Munna with the good natures, and then you can get great natures for all your team.
Flame Body (and Magma Armor, but nobody you can catch early in BW gets it) halves the amount of time it takes to hatch eggs. I think this might be the favorite ingame ability for most people.
Compoundeyes, in addition to being amazing on Galvantula, also increases the chance of Wild Pokemon holding an item by 50%. So no more taking forever to get that Nugget or what not.
These are the abilities I find most useful in Black and White, and for all but Mold Breaker, in all games.
