I've got three world states running for the series right now and they all have different PCs.
Canon:
Warden Aeducan - male dwarf; sword/shield warrior; dutiful, yet vengeful against those who wrong him; romanced Zevran
Garrett Hawke - male human; support spec mage; sarcastic, selfish, overly emotional mage loyalist; romanced Anders
Inquisitor Adaar - male qunari; two handed warrior; overly 'good' (almost stereotypically white-knight type); romanced Dorian
Alt World State 1:
Warden Brosca - female dwarf; ranged rogue; selfish, ruthless, cruel at times; romanced Leliana
Gavin Hawke - male human; sword/shield warrior; vehemently pro circle and anti blood magic; romanced Fenris
Inquisitor Cadash - male dwarf; dual wield rogue; charming, dashing, Robin Hood-esque scoundrel; romance Iron Bull
Alt World State 2:
Warden Aeducan - female dwarf; sword/shield warrior; knight in shining armor type; selfless; romanced Alistair
Marion Hawke - female human; ranged rogue; aggressive and sarcastic (kind of a tough gang gal); romanced Isabela
Inquisitor Cadash - female dwarf; ranged rogue; pro-circle; 'makes tough decisions for the greater good' type; romanced Blackwall
All different (as much as possible since there are really not that many choices on how to play) and all leading a different set of world state choices. It's why I'm not a huge fan of DA2. I felt that there was just less that I could do with Hawke than the others. In fact, I never even finished my Marion Hawke play through. I got her to the end of Chapter 1 and got bored with it. Just ended up choosing a different set of choices in the Keep.
There are a couple of constants, though. I never play elves (yawn). I rarely play mages. And all of my canon PCs are gay males. Outside of that, it's kind of open. I've yet to have a straight male PC, but I'll probably give that a whirl at some point. Although, if Cassandra (who I adore) wasn't enough to tempt me, maybe I won't.
Thinking forward, I'll probably do something like this for DA4 (if these choices are allowed):
Canon - male dwarf ranged rogue; 'tough', 'aggressive', and 'forceful'
Alt 1 - male qunari mage; 'good', 'scholarly', 'erudite'
Alt 2 - female dwarf sword/shield warrior, 'good', 'sarcastic', 'Mary Sue' type