I live across town from my parents (less than a 10 minute drive). As mentioned above, there are pros and cons, which change as time goes by. When my son was little, they would take him to the school bus for me, since I had to leave for work early, and the bus stop was across town (too far to walk). Now, if my mom needs to drop off a car at the shop (Dad isn't currently driving), my son or I can give her a ride to/from. I can pick up something from the store on "my side" of town, and drop it off for them. My mom will sometimes pick up some fabric for me (I quilt, she works at the fabric store). Sometimes we don't talk/see each other for weeks, sometimes it's several days in a row that we see them.
My son and I help them out with their yard and garden in the summer. Sometimes my dad cooks extra food and calls me to come pick some up. We can buy stuff in bulk and split it. He has called me to take him to the ER when my mom has been at work. They've let me borrow their car when I needed (when both truck and car are out of commission).
It's nice to have someone to check on the house/take care of pets during vacations.
I don't know that I could live next door to them, as my dad can get really nosy. Also, being single, once my son has moved out, I don't care to have my parents following any coming and going from the house (if it were to happen). I really like my privacy. If I did live next door, I'd want a lot of trees or a privacy fence in between the houses, with a front door facing away from their house.