Long ago back on Lawn Guyland my group used to play some superhero roleplaying games, particularly Villains & Vigilantes. (We don't play that genre anymore because not all members of my current group like it.) After a while I discovered that my favorite part was often making new characters with new combinations of powers. V&V allowed both choosing powers to fit a theme, and randomly selecting powers and trying to find a theme to fit them; the latter seems like it would lead to a lot of jumbled messes of thematically incompatible powers, and that was certainly sometimes the case, but surprisingly often, even a seemingly-incompatible set of powers can coalesce into an unexpected but compelling theme; and the process of trying to find that theme is an interesting creative challenge.
After a while, I had an idea for the best character idea because it gave me tons of chances to go through that. I named him Variable, and his power was that, every so often and for reasons as yet undetermined, he got a new set of powers. Sometimes I would pick a set, and sometimes I would roll them, and sometimes I'd roll a few and then pick a few to round them out.
This also gave me the chance to try out character ideas you wouldn't want to play for very long, but which are fun to play for a short time. The best of these was playing Letterman, from the Electric Company: he could change things by adding, removing, or changing letters in their names, though he had to use the same letter in every action during a single scene. This was way too goofy to sustain (once I stopped some villains from escaping on a boat by changing the dock to a duck) so this power didn't last long. But it was fun, funny, and surprisingly challenging: it seems very powerful but it's actually hard to come up with useful things to do.
The campaign didn't last that long because the group broke up, so later I reinvented the character for a play-by-email game and this time I came up with a reason, having to do with the effect of quantum indeterminancy on the biological process of cell diversification. As with most PBEMs, though, it barely even started before it tanked.
If I ever get to play another superhero game, particularly a four-color style, I will almost certainly try to revive the idea again. How could I pass up the chance?