The Pickup ability can be applied to a handful of Pokemon. Depending on the Pokemon's level there is a chance that a Pokemon with Pickup can 'pick up' an item.
The higher the Pokemon's level, the easier it is to get a rarer item. For example, in Black and White a Pokemon between Level 21 and Level 30 has a rare chance of getting a Rare Candy, but it's a common chance that it will pick up a Rare Candy if it is Level 91 to Level 100.
There is a 10% chance (1 in 10 chance) that your Pokemon will pick up an item after a battle, if it's not holding one already. Here are the items that can be obtained through Pickup. The percentages on the page aren't mathematically correct since they don't add up to 100%, so you can just substitute the percentages with stuff like 'Common', 'Uncommon', 'Rare' or whatever the heck you wish. xD
The Pokemon that can learn this helpful ability are Meowth, Aipom, Teddiursa, Phanpy, Zigzagoon, Linoone, Pachirisu, Munchlax, Ampibom and Lillipup.
Hope I helped. :)
Source: Above Link and Zis.