One of the funniest things I've noticed about having a child is not how it has affected us, but how it has affected our parents. We seem to have ceased being their children and instead have become grandchild delivery systems.
Phone conversations are completely different. "How are you?" "What's new in your life?" "How are things going?" have been replaced with "How's my grandbaby?" "How's the baby doing?" "Are you sure the baby's OK?" Mysterious boxes arrive from points unknown with fuzzy pink things inside so cute they'll turn your teeth into sugar. Visits from parents turn into home improvement projects, even gardening expeditions, and you'd be glad for the help except for this scary gleam in their eye. Looking there, you know they're not seeing you, but rather they're seeing the people who'll be raising their grandchild.
I guess part of the reason is grandchildren are the ultimate "other people's kid." They are yours in a very real way, yet if you get tired of them you can (usually) give them back. What's more, unlike other people's kids, you can give advice on how these are raised and the other party has to listen.
It's especially funny to see how nice they are to the kids. Things my nephew does that would've gotten my brother in trouble are just cooed over, "isn't that cute?" I get this terrible feeling that if my daughter poured a bottle of chocolate syrup on our couch my mother-in-law would smile and hand her a spoon. Bill Cosby was definitely on the money when he said, "These are not the same people I grew up with! These are old people, trying to get into heaven!"
And you don't dare actually give them your children unsupervised. Not because they'd do anything wrong, far from it. I only too well remember, after upending yet another bottle of model paint on my new school pants, my mother saying, "one day you're going to have kids. And one day I'm going to get to keep them, and on that day I will spoil them absolutely, completely rotten, give them everything and anything they want, and then give them back to you." I know this will work, I know it will, because, looking back, I realize that is exactly what my grandmother did to me.
Of course, there's also the parent's curse... everyone say it with me now, "one day I hope you have kids, and I hope they act just like you." At the time you thought it was a silly threat, and pitched a fit anyway. Decades later, you can see the holy terror that was you at that age, and you fear.
Don't think that your parents won't be that way just because they claim not to want grandchildren. Trust me, they're lying. My step mom, my mom, and my mother-in-law all actively discouraged their kids from having their first grandkid. Tell them the news though, and it's like someone set a happy-bomb off inside their head. And God help you if your brother or sister has a grandkid and you don't. Babies are like crack to old people, and it doesn't take long before they start jonesing for another one. From there it's just a short hop to, "you know, it's so sad, seeing as how I'm going to die soon and all, that I won't ever get to see your child."
You shouldn't really worry too much though. Having someone around who's already been through it all can be a godsend. Especially since they've been through it all with someone who's going to act just like you.