I didn't expect to want to.
My wife originally wanted to, and like you, I was... reticent. My feelings at the time seem similar to yours here.
All I can say is, having a solid partner -- one that I can absolutely count on, and believe in -- helped me unwind. I was able to set aside my original concerns and think long-term.
Here's where we may differ: I've always loved playing with kids. There's something magical about seeing them learn things, interact with the world for the first time, and to just screw around and enjoy life without the normal adult concerns. After all, when you're a kid, you have endless time and all you want to do is play. Chilling with kids and playing games with them has always appealed to me.
There's also a stigma attached to that, when you're a male. If I was female, lots of people would feel "Oh, that's cute!" but when you're a man, I inevitably felt like I should hide that aspect of myself. After all, everyone knows that it's dangerous or creepy for older men to hang around with kids, right?
It wasn't till my wife's sister had kids of their own that I was able to get over this. Once they got to 2yo or so, it all clicked for me. I remember playing the "colors" game with Eloise -- she was quizzing me about the different crayon colors, and it was so cool to watch her learn about orange. I don't remember exactly what she learned, but it was sort of an "aha" moment of orange being halfway between yellow and red.
From then on, I was sold, and decided I wanted kids of my own. Wiping their butts and being woken up with screams will just be a part of the process for me, and I won't mind at all. (Easy to say that now, I'm sure.) But, for example, you probably feel the same way about cleaning out the litterbox for your kitty; an annoyance, sure, but it's a labor of love.
That labor of love is a strength for me. It's what allowed me to ultimately be fine with abandoning my old (current) way of life and return to "the daily grind," as people might like to call it. My wife and I have been trying to have kids for a couple years, and haven't had success. I always felt like, well, whenever the kids come around, I'll go get a traditional job and be family guy. But then one night, I realized "You know, IVF is hugely expensive. I could go get a job right now, and we'd save up enough to get it done within just a few months."
It wasn't an easy decision, but once I made it, it was easy to follow. I want some kiddos to teach things to, hang out with, and occasionally learn from. My motives are no more complicated than that.
You'll feel differently. If you're young, all I can say is, expect yourself to change over time. The only thing you can count on is that how you feel today probably won't be your feelings forever.
If you're less young, then there's really nothing wrong with not having kids. There's a stigma against that too, which I think is bogus. It's simply a question of what you want out of life.
By the time http://www.paulgraham.com/kids.html came out, I was nodding along with that entire essay. Perhaps it'll help elucidate some of the feelings here. But a simpler way to put it is, "one day something activated in my brain -- some kind of primal instinct -- and from then till now, the desire to have kids has been a source of strength."