Not a parent, but I can tell you my parents' reason! I was a well-behaved baby. Almost unnaturally so. My parents were pretty certain they'd get a demonbaby the next time out, so decided that my being an only child would be FINE.
On the other hand, my brother and sister in law say that if their first or first two babies had been as good as their third they would have tried to have many, many more babies.
That reminds me of the great Cosby routine about the birth of his first child. He and his wife were delighted, because she was perfect: "Ding! My name is Erika, and I love you both. Mommy, what time would you like to get up in the morning?" "Um, 7:00?" "Well, I will not wake up until 9, and even if my diaper is wet, I will not even cry. I'll just lay there, saying, 'Leeleelilo, lilolilo.' My name is Erika, and I love you both. Ding!"
He then says that they decide to have another one right away, before they lose whatever they have going for them. Sure enough, Daughter #2 arrives, or as they came to call her, Beelzebub. Champagne in one hand, cigarette in the other, saying "Who's in charge here? You, the ugly guy, why are you here?" "I'm your dad." "Get rid of him, Momsy...What time ya been getting up in the morning?" "Um, 7:00." "Would you believe--3:30. And this is how I cry. WAAAAAAHHHHH!!"
The nephews' parents want to know why they got the easy one in their late 20s when they had all the energy and the difficult one in their late 30's when they were too tired for him.
On behalf of unexpected second children born with perfect well-behaved siblings everywhere, I would like to say, "Hey!"
I know that I was a planned second child. The only thing unplanned about me was that they wanted me born a few months earlier, but my mom got bronchitis at the time they would need to conceive, so I got put off for a few months. I'm not entirely sure why my mother thought I needed to know that.
Mom told us that my brother (born in '61) was a rhythm baby, and my sis and I (born in '64 and '66) were Pill babies. The dosage in the Pill was so high back then that a woman usually had to wait three months after going off of it before she got pregnant, but she conceived me within a few weeks, so I ended up being a few months earlier than originally planned.
I don't think that more siblings mean more people to take care of aging parents is anything to count on. In my experience, one person, usually a woman, ends up taking care of parents, while the other siblings make sympathetic noises. In my case, I'll end up taking care of my sister.
My parents have said that as babies, my sister (middle child) was "loudly stubborn." I (youngest of three) was "quietly stubborn." We were equally a handful, but I just didn't make as much noise. My subversion was much more stealthy. That pattern has persisted all of our lives--sis is very outgoing and you always know what she's thinking. I tend to retreat into a hole and not come out when I'm depressed/sulking/mad. Turns out, I'm more difficult to handle in the end.
Oh, and I found a store near me that sells used furniture, and it's run by a rehabilitation program for prisoners -- prisoners at a nearby prison take a class in conflict resolution and interpersonal skills, and then they staff this store and connect with the community, instead of spending their prison time totally separated from everybody else. I bought a rocking chair for my front porch. The chair desperately needs a new coat of paint, but so does the porch, so I guess it matches. Maybe I'll buy some paint and make the chair pretty some weekend when I'm bored.