When I'm in love, it pretty much starts with non-sexual affection... What I think about is hugging, holding hands, cuddling... Actually, until I start a relationship, often it's like I'm not allowing myself to have sexual fantasies "without their consent".
Now, I realise doing so wouldn't be a problem, and I do have fantasies about perfect strangers, etc, but I guess what I mean is that they're so elevated in my mind that "base" feelings like sexuality are barely relevant. I love them on a different level.
I'm not sure if I'm making sense here. My point is that non-sexual affection sounds very much normal to me. When I develop feelings for people, it either start with non-sexual affection (sometimes with a small dose of sexual attraction too, but it's never on the front of my mind) or with sexual attraction. The first type is the one that has turned into long-term relationships for me. The other one has evolved into either a friend with benefits (has happened once) or (most of the time) nothing at all.