Lets see: 
  
Witcher Series 
Gothic Series 
Two Words Series 
  
Many more I can't think of at the moment I haven't played because I'm only interested in female protagonists.  
  
Dragon Age Origins (II and I arn't speaking) 
Mass Effect Series 
Jade Empire (There may have been a heavy style for men and a fast style for women and a balanced style for both. I'm not sure) 
Neverwinter Nights (2 an Obsidian Game, would you beleive!) 
Knights of the Old Republic 1 and 2 (Obsidian!) 
The Elder Scrolls 
Most of the Ultima Series 
Fallout Games 
All infinity engine games except Planescape to my knowledge 
Even Minecraft and Terraria allow avatar customization 
Just about every single MMO ever 
  
  
  
This 'selection' thing is some old relic from shooting games and diablo (and revived with borderlands) 
  
From what I can tell 'pure mage' and 'pure warrior' are reserved for male archetypes while females get some hybrids. 
  
It seems by my reckoning that if DSIII is an action based game it shouldn't matter so much about the characters irrelevant personal life histories, and if it is a true RPG then there should be some customization of basic details. 
  
I mean if the industry leaders Bioware and Bethesda can consistently offer us the choice..