Well first off, mine is AD Sona. Sona is soooo much fun as AD even though she is so squishy it's just fun watching the enemies health go down so quickly. So what's your favorite champion to play as in a different role?

AP Nunu if your opponent has no cc. It's awesome seeing that ulti damage :P

Quite possibly one of the most hilarious i have ever tried was ad Morgana. with her binding no one escapes and thanks to her shield ap's aren't as much of a problem, with those and her ulti she is just so ridiculously silly as ad.

it's arguable how off-role it is : support-tanky ashe.
Not quite a dedicated build, when I'm left ad carry with no real support (you know those pantheon/volis/mundo). I grab ashe, if I can,t play carry for some reason (like a voli taking all the ks because he hits harder than me), I'll grab gp5/tanky item and let him carry. When teamfights comes I can with some luck harass, snare and survive some burst.

If the game drags on, I,ll eventually transition into ad. But I,ve finished games in 30 min building tanky ashe with gp5.