I'll separate favorites into what type of champion they are (Support, AP Carry, AD Carry, etc)
Support - I played Orianna as a support with decent AP damage. Although she isn't listed as a support, her skills seem to make that option viable.
AD Carry - Kog'Maw, because he's got good range and INSANE damage if you build him correctly.
AP Carry - Although I love many, Zyra and Ahri are the favorites. Zyra's got great burst damage and a fast combo, while Ahri has pretty good sustain and damage to boot.
Tank - I don't really play tanks, but I enjoy playing Garen and Cho'Gath (yes, I consider him to be tanky) every once in a while.
Jungler - ??? I don't jungle, since I don't have the runes and masteries to support it yet. I've been told that Evelynn is a jungler, and I do like her. Soooooooo... yeah?