In my opinion, you shouldn't focus on the age, but the maturity. You can have a fourteen year old that acts older, or an eighteen year old that is immature. Unless you're worried about them being old enough to drive. Then You have to take both age & maturity into consideration.
I think a lot depends on the babysitter - I was pretty mature when I was a kid and the oldest of 5. I was looking after my younger siblings for short stretches when I was 8 and babysitting other kids at age 12.
I wouldn't let any child babysit one of my kids. Period. I've only had one person ever babysit my kids. I've known her for 10 years and she's also a mother of 4. I wouldn't ever even consider someone watching my children if I didn't know them and if they weren't parents themselves.