RPGMemes

I was totally going to reference this myself and you beat me to it.

This is actually sort of similar to my usual character creation process. I start with some basic concept and/or gimmick that's usually a little bit silly, corny, intentionally weird, etc, then I add to it until I've built a proper character around that goofy idea. I made an "anti-edgelord" bubbly church girl cleric that inadvertantly became a badass magical girl and grizzled war veteran. A barbarian that wears clothes made entirely from skunk skins and acts like a wise woodsman calling himself "the striped sage" even though he's mostly full of crap (but really good at hitting things with an axe). A rogue fleeing his home city because he got the sheriff's daughter pregnant while she was in a rebellious phase and slumming it with riffraff (her father is very unhappy). Most recently a druid with the noble background and concept of "rich kid college dropout runaway vagrant hippy chick" that the DM approved "but you're not just a noble you're a full on runaway princess."

You get a clear gimmick to start with that works as an icebreaker with the party and an easy beginning point for roleplaying. You can play up that gimmick as much as you want to, or even hint at it and make it something your character is obviously trying to hide or minimize. Once the gimmick is established you start adding the serious parts you've built up around the gimmick. Conversely you could introduce them as a straight laced, serious character then start hinting at the weird gimmick or just spring it on everybody at an unexpected time to get that wonderful WTF reaction when the other players notice it. Either way it gives you a solid starting point that you can build and develop your character from as they interact with other PCs and the world in general.

Edit: This method also works great for making memorable NPCs if you're the DM. Take the basic narrative function you need the NPC for (merchant, quest giver, distressed citizen, local lord/lady, etc) give them a mildly weird gimmick that will stick in players' minds.