I do worry sometimes about "dying alone" and that sort of thing and I worry about whether I'll find a lasting relationship. But I haven't staked my happiness on getting married. As for kids, I don't seem to have much of a natural desire for them. I would definitely think only in terms of "maybe it could happen if I found the right guy, and we both wanted kids." Though I tend to feel like I would rather be happily childlessly married, but I know that can change when you're with someone you love. But I would rather be single and even not entirely happy (ideally happy and content, but that's not always possible) than unhappily married. And fortunately my parents don't pressure me to get married and start a family, they just want me to be as happy as possible.
The only thing I would say is that this is probably a bit age- dependent or related. I'm 32. In other words, if I wanted to have kids I would have to think about it relatively soon. This has occurred to me a number of times lately. Not in a sort of "oh noooo, biological clock" way, because I honestly think I'm less drawn to babies and children than many or most women. Just in a sort of...hmm, my options are closing down a little bit way. Which isn't the most wonderful thought even if I'm not dying to have kids.