DAI: What we know so far. Cullen has seen the worst of both sides, and arguably the best of both sides. Where his character arc goes next I suspect depends on the ethics of our inquisitor.
So, what I get from that is a character with strong willpower, a high standard of ethics, he's not afraid to fight for what he believes in, and acts in a gentlemanly manner even if he doesn't agree with you (My mage Hawke loves trolling him).
I like his character, the looks are just icing. 
I know lots of people have already chimed in, but I would agree with this. I wasn't a fan since the mage origin, personally - I played a mage maybe 3rd or 4th, and even then I managed to not quite get that he was seriously crushing on her until about half-way through the discussion when he's trapped by Uldred. By then, I had pretty much pegged him as that poor templar who was tortured to the edge of sanity. The events with the mage origin just made it more personal for her.
I didn't play far enough in DA2 to talk much with him, either.
So mostly, once I heard that DA:I was about to release and decided to do some research, one of the primary things I was interested in was learning about the major characters' backgrounds. After reading wiki entries and watching youtube videos of his scenes from DA2, I got a lot more interested in the character himself. He's gone through a lot of major events, and personally experienced both ends of the spectrum in the templar-mage conflict. He has also proven himself to be strong-willed, principled (even when I would have disagreed with his stance), and courteous. These are traits I admire in people in general. The only time he really seemed to go off the deep end was after being tortured for days and perhaps weeks (or months - it can take me a while in my play throughs to get to the Circle Tower - heh).
To be honest, I didn't think the pictures of him on the site were very attractive at the time I started to poke around, and did about the same amount of research as I did for Varric and Cassandra (as there were similar amounts of info out there for them). It's only after I did this research that I thought he was pretty attractive - though admittedly, they also had new screenshots that were more flattering so that might have had something to do with it.
As to virginity, a lot of other people have covered it sufficiently, and I don't have anything to add aside from I agree it's unlikely, but it wouldn't bother me either way.