I have a ton of ideas that I would love to play, but, upon slamming into the rules and setting, invariably find out that I 'can't do that' or that 'it doesn't fit,' and that I'd enjoy the game more if I wasn't banging my head against a wall trying to fit a square peg into a round hole.
And so I read over the rules and setting and find something there that jumps out at me. I end up making lists as I read through a setting book of ideas that just leap out at me as cool (one Greyhawk product mentions that in the lands of the Snow Barbarians, there are occasionally pale albino warrior maidens who tend to be loners, associate with wolves and are most typically rangers or druids, that just screamed out 'cool!' to me, and that went on the list of characters to someday play in that setting. Each setting has throwaway lines like that worked into it that similarly inspire, and some, like Al-Qadim, are *dripping* with inspiring character ideas).
Happens in RPGs, happens in online games. I joined City of Heroes and immediately found out that I really couldn't mimic some of my favorite superhero characters from Aberrant, GURPS Supers and Villains & Vigilantes games past, but that the world itself, the various locations, power groups and organizations, and the powers that were available, lent themselves to dozens of awesomely fun ideas. Instead of being the lame-o who tries to squeeze Drizzt or Wolverine or Chuck Norris into some other setting, or some other rules-system, it's far more fun for me to find something in the setting that oozes coolness and screams 'play me, fool!'
Whether the world is the Zakhara, Trinity's 2120 future, Golarion, the old school World of Darkness, or the Scarred Lands, each world has it's totally cool areas, races, factions, etc. to play with.
And yeah, it's pretty much a given that you have to consider the other people at the table. Moody loners who contribute nothing to anyone elses fun and monopolize gametime with their solo-exploits, and restrictive moralists who try to enforce some sort of code of behavior on everyone elses characters because of their horribly selfish team-unfriendly character choice are right out. I happen to love playing healers, whether Clerics and Druids in D&D, or Defenders, Controllers and Masterminds in City of Heroes, or Shamen, Furies and Defilers in EverQuest II, so I've never felt like I had to 'take one for the team' by playing a healer, but there are times when the character I really wanted to play turns out to be redundant, grossly overpowered compared to another player, or grossly innappropriate for the adventure at hand (sure, you can play an Aquatic Elf in the Desert of Desolation or a Specialist Conjurer in the World's Largest Dungeon, but why the hell would you want to?).
At that point, I just break it down into a subset of character ideas that both suit the team / adventure / game at hand, and that I would like to play. Fortunately, the list of characters I would like to play is extensive, and I went to Xendrik Expeditions at GenCon with eleven different characters, representing all factions (and a few undesignated ones that could plug into any faction), written up at both 4th and 6th level (since I wasn't sure which one I'd want to play in the higher level game). Sure, it takes 15 minutes to bang out each character, so I probably blew a lazy Sunday afternoon doing them up, when I could have been doing something equally trivial like watching a couple of episodes of Heroes and getting worked up over how freaking stupid all of the characters are, but I enjoyed the process, and it gets faster as you go (and adding 2 levels to them to make the 6th level versions is ridiculously fast. Cut-n-paste, up some numbers, get another feat, add better gear and good to go).
About the only time I end up playing something I don't like is at conventions, where I traditionally try out games I've never played before, and end up at a table with some experienced players, who snatch up any pregen worth playing and leave me with something awful, which I try to remember doesn't necessarily mean that the game system sucks, just because my first experience at the game sucked...