In my opinion, it'll be way difficult to impose a strict bedtime for a 15-year-old. I think high school is a time to let children start setting their own boundaries based on the consequences they experience from their own choices. In other words, if they want to stay up until 3 am, fine, but when they don't want to wake up for school and they're tired all day, they'll rethink that choice the following night. Of course, mom and dad will always pop in and say things like, "Honey, it's getting late. Don't you think you ought to be going to bed?" However, high schoolers will find a way to stay up late anyway.
If you absolutely MUST set a bedtime, though, I'd say 11 pm is a decent one. I think any child in elementary school should be going to bed by 9 pm. In middle school, perhaps 10 pm.
Here's another way to think about it. It's suggested that people get 8 hours of sleep, so you can subtract 8 hours from whatever time your kids have to get up in the morning. So, if they're up at 6 am, they need to be in bed by 10 pm. If they're up at 8 am, they need to be in bed by midnight. Of course, younger kids need (and usually get) more sleep, but this may work as they get older.