hmm, haven't played that many champs (and own only 1 atm), but I try mine...
(And I don't know / care if those champs aren't normally played that way or not)
Top: I'm worst playing alone ^^' (maybe 'cause 1 vs 2?), but played a few times as Braum, Nunu, Cho'Gath, Kog'Maw,
or Volibear (kinda disappointed with Volibear, thought he was more interesting, but that ult is kinda boring)
Mid: Singed, Thresh, Nunu, Cho'Gath, Kog'Maw,
(it's been a while since I played mid...)
Bot/Sup: Braum (I like to play with him the most, bought him with ip),
Nautilus (maybe I have to play a bit more often with him, buying him next), Thresh, Singed,
Nami (didn't like her that much 'cause I can't play squishy support, I like tanks / offtanks),
(I'd like to try out Galio or Tahm Kench),
Jungl: (I don't like being Jungler, but played it a few times) Skarner, Kog'Maw,
(maybe try it again with Rammus, when it is his time for the rotation tryout)