Two/three I found could be played asexually.
Josephine. Focus on purely on the romance portion - banter, honour, grand gestures, wooing. Thus the colloquial title of 'Disney romance'. Available for all races and both genders. I find it so sweet it almost hurts my teeth to watch. Love it.
Blackwall. For this one, when you drink at the tavern, one of the flirts involves staying at the bar (but is still considering a flirt!). Personally I loved that option, lead to my favourite line from Blackwall in the entire damn game in fact. Don't want to spoil it for you. Damn good. Integrates well into his personal story, but being an optional character doesn't mean anything in the way of the story.
Solas also gets a note for keeping sexual liaisons ambiguous (it is up to you if they did anything offscreen, there is never a fade-to-black). The reason for the 'two/three' as if I don't quite count him, is that there is still a lot of passion present so if that's not something that floats your boat one might find it intimidating or overtly forward. (No actual sex happens, but making out is like... the first thing the romance involves.) The use of deliberately ambiguous lines may interfere with or enhance your role-play depending on how you take them.
Still very sweet and respectful though, and a lot of peeps on the BSN are apparently incapable of romancing anyone else afterwards. (Also if you ever watched Torchwood he's Ianto Jones, so that can make some stuff hilarious and/or weird, such as his hatred of tea even though he makes it all the damn time XD)
Romancing Solas doesn't affect the plot anymore than having him in your party would, but he DOES provide commentary on your Dalish heritage and the Dalish way of life that you wouldn't get platonically.
I think it is also possible to romance Dorian without sex. He enters your room expecting it, but you can refuse and say you want to know him first (which does surprise him). I can't say for sure that stays throughout the game though. I think it does.
Personally I was very glad of these options, because in DA2 the LIs tended to arrive just after my mother died and if I didn't bone them RIGHT THEN it was because I was breaking up with them. Thought that was a depressingly one-dimensional way to look at relationships.