Character creation.
For me, character creation starts out with a hook...some kind of storyline that will make this an interesting and intriguing character to play. What that hook is depends on the game, where I am mentally and emotionally at the time, what movies/books/tv shows have made an impression on me...
And it doesn't have to be a big thing. It can be subtle things, like he was picked on as a kid because nobody knew who his father was (it's a Scion game, his father was a Norse god...but you can't go around telling your kid that, because when he tells people you told him that, they come visiting with medications and funny jackets to take you to visit a nice man who wants to know what event in your life induced this delusion...) That builds into a kid who got picked on, until he learned to fight back...and, being a Scion, he's stronger than the other kids, so the bullies learned to leave him alone. So he started making the bullies leave other kids alone, because they didn't deserve it. That turned into an interest in law enforcement and justice...so he becomes an FBI agent.
Or he's a sniper. Snipers are notorious for being a little different, emotionally, very comfortable being alone in their own heads and very self-reliant. Why would he have developed this? Well, his mom and dad divorced, his dad remarried a Navajo woman, but being a white kid on the reservation put him in a minority position. He never really clicked with his stepmom, grew distant from his dad...not much to do on the reservation besides camping, hunting, etc (depending on where you are...some places have more to do than that, but there's an awful lot of open land out there, too...) So, he spent more and more time away from home, out on his own. Got old enough to join the military, it was a free ticket out of there, and he's already had years of shooting, stalking game, living on his own off the land...he could go Special Forces but that's too social for him, so he goes Sniper. When he gets picked for a special mission task force, he's got to learn how to socialize with the other task force members...which gives me some 'meat' to roleplay outside of the combat engagements.
I figure out who I want my character to be, and then figure out what made him that way. I tend to do 'generalist' characters, who may be competent at several things, but are rarely outstanding at any one thing...they're self-reliant, as much as possible, but they also fit in with just about any group. But if my character has some outstanding skill or trait, I make sure there's a logical reason for it in his background. I know some people who build their character specifically with fighting in mind, or magic (if it's in the game), or whatever...I generally don't do that. If I'm going to make a character that's geared strictly to combat, he's going to have been raised as a gladiator all his life, or grew up in Sparta (or whatever the equivalent would be in that particular game setting)...I try to come up with some motivating factor or solid explanation for his abilities...and if I wind up needing to knock some points off his 'great' abilities in order to pick up some lesser abilities that would make sense, I will. I prefer plausible characters (even if that plausibility gets stretched pretty thin sometimes...*looks at his Troll Martial Artist character from his Palladium Fantasy days*) over spectacular characters. Part of that is the GMs I played with throughout high school and college...in their games, if you made a character that was inhumanly strong but too dumb to figure out a doorknob, that character either broke down a lot of doors, or spent a lot of time trapped in a room until a smarter character opened the door for him. Yeah, they'd let you play a combat monster that was too stupid to know how to take his own armor off at night...but whatever attribute you sacrificed in order to get that strong? They would use that to make you pay, time after time after time.
So, that's always in the back of my mind as I build characters...well-rounded, unless I want him to suffer constant humiliation over whatever I designated as his 'dump stat'. Plausible explanations for special abilities, or for normal abilities developed to an unusual level. And I usually put together at least a basic life history...a lot of details evolve and become more clear as I play the character, and I don't like to try and sew up all the loose ends in a nice, tidy bundle. I leave a lot of material unclear or dangling for the GM to turn into story hooks if they so desire.
The last thing I try to figure out? The character's motivation for being there, in the first place. Sometimes it's easy. Sometimes, the GM looks at what I've given him and says, "Okay, you are here, and this is why," and I don't have to worry about it. But I try to make sure my character has SOME reason to be willing to run around with all these other guys...