I wouldn't date a single parent. Certainly not at this stage in my life. In general, I prefer someone who has a similar outlook on life and who has had similar life experiences. I feel I wouldn't share that with someone who is a single parent. Having a child vastly changes your perspective and reshuffles your priorities. I think it is hard enough being a busy adult and squeezing in time to spend getting to know a new partner; having to further divide that time caring for a child would be extremely difficult and taxing on a budding relationship.
The other thing that dissuades me is the idea of the consequences of developing a bond with the child (or children) of that partner. What happens when you and your beau decide to call it quits? It's hard enough as it is going you separate ways when things do not work out. Adding a child to that equation would make it even more difficult (at least for me).
Finally, wherever there are children, the ex is usually still somewhere in the picture. I've seen my own mother struggle with this, as well as a few of my girlfriends. It is rare to see a civil arrangement between two separated parents and it weighs down emotionally not only on your partner, but by extension, you as well. And the thing is, if they both care about the child, they're bond like this for the rest of their lives. Not just legally, but emotionally as well. The family from both sides is sometimes involved too, in which case, you are always seen as the intruder, the person standing in the way of these two people making it work for their children. Not always so overtly, but on some level, it's always there.
Maybe this sounds awful, but all that is just simply too much baggage and I've had enough dysfunction (and seen enough of it) in my family to invite it into my romantic life. If I have children, it's going to be a decision made by my partner and myself. I don't think I'd have the emotional maturity or psychological strength to raise someone else's kid, let alone put up with all the ancillary consequences of entering into that kid's life. There are stronger people out there who can do that, but i'm not one of them.