Great responses, and interesting thread Thalia!
As a single Mom with three kids, I really DIDN'T "date" for a good while after my divorce. (Of course, I'm in that "old person" catagory, so take my opinion with a grain of salt...).
I was cautious for exactly the reasons many of you have listed: It would be hard on my kids having a parade of men through their life, it might be hard on one of my dates if he immediately "bonded" with my kids, and in view of my rather conservative standards, I didn't think it would set a good example at all. Plus, I'm hyper-over-protective anyway, AND two of my kids are teens and were ADAMANT that there were going to be "no men in our house" due to bad experiences we'd all just been through...
Well, we can fast forward about 5 years... I met "someone" online and I was very upfront about the fact that I had kids right from the start. (I'd have to be, my kids are my LIFE) and I talked about them and all, but didn't introduce him to them face-to-face for about a year. (Which was easier for us than for some relationships, since we're doing the whole long-distance thing...).
I told my kids about him about five-six months into the relationship however, so my kids knew about him and could ask questions and everything, long before they had to spend any time together - which worked well, timing-wise for my kids, I knew they'd be a REALLY hard-sell.
If I just had younger children, or was dating someone local that I saw every day, I might approach the whole thing differently, but I would still wait until we were definitely "serious" and committed to something long-term before I let them meet my kids.
All that said, my kids really like Froggy and he adores them and it's all worked out SOOO well.
Take it slow, and if you aren't sure of the commitment or permanancy of the relationship, do yourself and the kids (theirs or yours) a favor and DON'T MEET until you are fairly sure you'll be around for a while. It doesn't mean you have to stay around forever, obviously things don't always work... but take their hearts (and yours) into account!