I spent a moderate amount of time customizing characters for Saints Row 3 (actually, most of my time with the "Initiation Station" character creation tool was spent Nancy Drew-ing why it was telling me my pretty unique name, "thriceberg", was taken. It was a big mess, I think having something to do with my using it once with a THQ account. I don't even remember how I got it sorted out.). Then I went to SaintsRow.com and saw all the cool characters other people have made. I ended up using other people's models, occasionally tweaking to suit my desires.
I was browsing the models in preparation for Saints Row 4 (which can use the same character models as SR3. Thanks, Volition!) and saw there are quite a few good ones. I'm going to link to the pages, but I suspect the web site's age verification wall will forget links (it did during SR3's release). So I'm also going to include a picture. If the creators of these models has a problem with that, let me know in the comments and I'll take them down. That said, if I could see them in the first place that means they were set up to be public, so it shouldn't be a problem.
Elizabeth from Bioshock Infinite
There are a ton of Elizabeths on the website, but this one is my favorite.
Kind of uncanny, I think.
You'll notice how any character you make in a Saints Row game always ends up looking at least a little seedy, even Jedi.
And an oldie but a goodie:
Notice that they substituted a picture of a skull instead of chest-hair shaped like Australia, but it still works.
There's plenty of other awesome characters, but these are the ones that have jumped out at me. I usually play as a non-referential character, just someone that has a cool look. Playing as Elizabeth or Saxton Hale would be a little weird. Playing as Nicolas Cage...well, that kind of makes sense.
I do hope that the promised modding tools for the PC version will allow people to add their own clothes and tattoos and such, but I'm not holding my breath over it.