Probably an unpopular view but...
Personally, I wouldn't ever take any of my child's gifted or earned money and require it to be put into savings, especially not towards something specific like college. Any money my children earn or are given is their own, to do with as they choose. Certainly I would encourage them to save money -- particularly if they plan to attend college -- and I'd help them think about the best way to go about that, whether it was by putting it into a 529, a high-yield savings account, a CD, or what-have-you. But required savings? Not a chance.
Which is not to say that we'd give our kids a free ride through college, either. Our current plan is to match each of our children's savings (the ratio at which we match will depend on our income) and to give them access to all of that money on their 18th birthdays, although they could withdraw the amount they themselves contributed before then. While we would advise them to put it towards something with a good return -- college, a car, a down payment on a house, starting a business, or even world travel -- we're not going to be all that upset if they blow it, either. Honestly, if that's what they choose, then it is probably a lesson they need in what happens to money if you don't spend it wisely.
DH and I are a big believer in 18 as adulthood and would feel that we had made some serious mistakes if our kids were not prepared to move out and be adults at 18. In fact, we'd be making some serious changes if we didn't feel our kids were ready for that responsibility at 16 or 17.
We also don't believe that college should be the goal for all young adults, and frankly, both of us would rather that our kids worked and lived on their own for a few years before starting college (if they decide to go at all). We will happily support whatever path they choose in life (so long as it's legal and ethical).
I think this has a lot to do with our backgrounds, however. Neither of my parents have much in the way of education but had (and have) very fulfilling lives. My husband's parents both have Master's degrees and high-paying careers, but don't really seem all that happy or fulfilled. I moved out at 16 and was definitely prepared to "fly the coop" at that time. My father did offer to pay my way through college, but I thanked him for his generosity and declined. I've never regretted my decision to skip a college education and feel that I learned more valuable things through self-teaching and life experience than I would have by earning a degree.
My husband was pressured towards college and required to save a portion (half I think) of the money he was gifted as a child... he finally agreed to go when he was 20 but dropped out twice before it was all over. He's currently in his last semester and interviewing for jobs, and while it does look like college was the right choice for him, he resents the way his parents handled the issue (and many other things that they did "for his own good" both as a child and an adult).
Perhaps because his parents had always expected (or really, decided for him) that he would go to college right out of high school, live in a dorm, etc., he was not prepared for the real world when he moved in with me at 18 (I was 24). He had no idea how to go about renting an apartment, how to get electric and phone services, how to budget, how to cook, how to keep a home clean, etc.
But the biggest reason that neither of us would ever enforce savings for our child is based on my husband's relationship with his parents. It became more and more adversarial over the years, culminating when he moved out of his parents' home soon after his 18th birthday -- without so much as a goodbye -- and before finishing his senior year at high school. Enforcing savings was just one of many things that contributed to a huge power struggle between DH and his parents (which started while he was quite young -- certainly long before puberty). Even now, his relationship with his parents is strained.
Remember how I said he dropped out of college twice? Both times it was because his parents were contributing to his education and DH felt that he would never really be a free person until they stopped doing things for his own good, even though he was married, had a child, and lived 1,500 miles away.
I am 99% sure that I would have reacted similarly had my parents behaved like his, even though DH's parents didn't do anything that would be considered unusual today. I had one heck of a rebellious/independent streak; I still do, in fact

In any case, I'm not trying to tell anyone what to do. Only you (and your partner, if applicable) can decide what is best for your own family. But I did want to share why DH and I are making the decisions we are for ours.
Sorry for the long ramble.
Lisa1970, I think your idea is great. But if you're opening 529s in your own name that contain your teens' savings, I
personally believe that they should retain full access to the money. Also, congratulations on teaching your kids the value of saving money towards goals important to them.
--K