Of course they do. If they don't, in my opinion, they're not real men. There is the cultural aspect. As a rule, Western men are not taught to be 'cuddly'; they are the rock, the strong take-on-the-world types because that's what the culture calls for. Bloody shame, that.
Then there is the inability that many men have to separate sex from intimacy; the old 'don't start the engine if you don't want to drive the car' attitude. I can't think of many things that are better than quietly holding someone I really love. That is an end in itself, and does not need to lead to sex to be fulfilling.
I may be in a minority (obviously so, or the question wouldn't have been raised), but I'm a very touchy-feely kind of man where my love is concerned. If that makes me weird, then I'm weird.
That's my tuppence, and worth every bit of what you paid for it.