To me a character is based on a variety of factors including, but not limited to:

Fun, usefulness, uniqueness, playability and roleplayability

Fun means just that: fun. Fun for me is being able to roll the dice and in an average situation and have a 50% chance of success at whatever my character is supposed to do. So, if I am party face or skill monkey, against Ted the first level commoner, I want to be able to Bluff him with at least a 50% chance. Failing every time you attempt to do something is not fun to me. Neither is always succeeding.

Usefulness: The character needs to do something for the party, preferably something the party needs. So if we already have a fighter and mage and a thief, guess who needs to be a healer?

Uniqueness: How recently has someone in our group made a very similar/identical character? If fairly recent, then I shop around for other ideas.

Playability: This ties into fun. If I play a fighter and I make him an elf with with an 8 STR and a 6 CON then I am really not playable. It's fine if that's how your stats look after fighting some Lich or something, but to start your career off like that? Why?

Roleplayability: I have a very difficult time roleplaying stupid characters. It's not impossible, just difficult and I find it unpleasant. Thus I tend to assign stats based around having at least a 10 INT. I usually choose a race/class combination that makes sense for the setting, then I optimize it to point where it will be enjoyable, useful and playable, without being so illogical that it breaks character.