Like @SG and others, I start with a concept: rules-bound fighter pilot, foppish swashbuckler on an info-gathering mission, flirty mercenary out only for himself, defecting Imperial Army officer. This will usually also suggest what the character is going to do (the pilot is going to try to make sure others follow the rules and is going to fly, the swashbuckler will get involved in everything to get as much info as he can, the mercenary will flirt and will do most anything he's paid to do, the defector will join up with the Rebels and try to instill some professionalism into them), as well as their primary skill set. Alternatively, I could have a story that I want to tell (an honest Republic Senator seduced by the Empire), but in many ways that's a concept all on its own.
After that point, I start filling in some details in their background (the pilot's mom is a local politician so he grew up in relatively high society, the swashbuckler learned how to buckle swashes with the circus, the mercenary is hideously burned which makes it hard to flirt and makes him harder for it, the defector is a grav-ball nut and a closet geek with a tabletop wargame army he had to leave behind), which also lends itself to background skills if the system allows for them. This work also tends to inform a character's weaknesses (the pilot probably isn't much of a brawler, the swashbuckler probably doesn't go in for stealth, the mercenary isn't good at empathy, the defector isn't particularly doctrinially flexible). Some of these may be mechanical, some may be RP-only. This is also when quirks come up (the pilot is a stress smoker, the swashbuckler loves his hat, the mercenary has a gorgeous voice, the defector uses proper titles for everyone).
I like to leave the background relatively open-ended, because that's the best way to leave holes to fill with other players (get your minds out of the gutter). If you know exactly what your character has done in the past and why, not only do you get into the problem @Arkandel mentioned about having already done everything, but it's harder to mush around events you do know happened to arrange connections with other characters.
Sometimes I see the character's looks in my head immediately -- sometimes I even have a PB in mind while I'm designing them. Sometimes, however, I get to the end and have to think "What are the character's defining characteristics," like @ShelBeast was mentioning, and come up with a look based on that.
I will often re-use concepts, but the differences between games always make the character themselves different: I've used the flirty burned mercenary on what... 4 games now? 5? But on one, he was a hidden Seanchan agent infiltrating Andoran society as a Domani mercenary, on another he was a straight-up Seanchan warrior (who ended up a Rebel Warder, oddly enough), on another he was a simple Domani mercenary with no ties to the Seanchan, on another he was a Viking warrior traveling to England... I think that's it, just 4 versions.
There are a couple of tropes that my characters often fall into, because that's the sort of RP I like to get involved in. The plurality (maybe majority) of my characters are either a bombastic politician or a hardened soldier. That lets me get into either politics or combat storylines, and I enjoy playing those tropes. Luckily, they're pretty broad tropes, so the characters within them can be wildly different. I've also been known to go wildly outside them, like the naive would-be Aes Sedai, the sneak-thief, and the utter fop with no interest in combat and no skill in politics.
My characters also tend to talk a lot. I've played a few who don't, but I always have to struggle to cut words out of my poses and replace them with body language. Apparently, I like to communicate through text. Go figure.
As to @SG's comment on specialist vs well-rounded, I like to be "good" at one thing, and then 'not bad' at a bunch of others. This lets me be primary (or often secondary due to someone who really specialized) at one thing, and back people up at others without being useless. This is why I like open sheet games... it lets me see how specialized other characters are, and how well-rounded I can make my character while still being "good" at their specialty.