I'm a single/divorced man from a 13 year marriage. We never had any children. Talked about it, but she would divert the topic and not bring it up again.
I'm now talking with a woman, and we hit it off really well.. we've been talking on the phone for about a week. She has 3 kids. I have not met her yet, for she lives about 500 miles away from me. Which I actually think is a blessing, because it keeps the physical side out of the equation and helps us get to know more about each other. She agrees also.
I love cartoons, Toy Story, Scooby Doo and love Disney World, to go to the toy section and look at the different toys. I really consider myself a big kid. (I'm 38)
But friends and co-workers tend to steer me away from being with someone with kids. They just don't see me with kids, and being that dad role.
It's a little confusing. I love to do adult things, but have the kid inside me there also. I'm responsible, own my own home. Work FT with $ to save. Help 
and thank you...
To add about me, I consider myself very sensitive, have a great sense of humor and am very understanding... which could be a failing, because people tend to take advantage of that with me...
also, about the woman I'm talking with, I have seen pictures of her. and she is quite attractive, as she has seen mine and she seems attracted to me also. We want to meet, but will probably be in about a month.
Thank you all for the very insightful, understanding, and helpful responses... so many.
btw, the children ages are 4, 6, and 9.
As meeting with the kids, it really hasn't come up, which I agree with many of you.. wait for that. I do feel a connection with the woman, as to why I even am considering a future (and also asking this question).
Thank you all again, you all have helped very much!
Also to add, sorry there's a lot of responses.. I do like kids. Co-workers have brought them in, and I enjoy the company and they love to play with my desk toys. My friend also has a stepson and we played the wii when they visited..it was a blast...Thank you again...