Why do people ask how your baby was delivered? And want all the details? Isn't that just a tad too personal? What should I say next time someone asks what kind of delivery I had w/o being rude?

I'm guessing that it's mostly women that are asking this question. It's a way of making conversation. If they see you with a baby, they have the opportunity to bond with you over what kind of birth you had, how big was the baby, did you have a hard labor, how did you name your baby and etc.

Simply respond - "it was a natural birth and I didn't have any problems" and change the subject if it makes you uncomfortable. In this day and age, people feel they can ask about anything. Just be polite and move on. Simple as that.