If you don't think you'll need the money for anything, you might consider starting a retirement fund. If you start early, the compounding interest will make you unbelievable rich in 40 years. Here's a link to a great msn.com article that talks about "starting in your 20s to get rich" that's worth a read:
http://articles.moneycentral.msn.com/CollegeAndFamily/MoneyInYour20s/ToGetRichStartSavingInYour20s.aspx
Now, if retirement is too far away and you are looking at something short term, some banks have special promotional CDs geared for tweens and teens. These are called "Youth CDs" and are 1 year CDs with a 1.45% interest return. Of all the investment options I looked at for my teens, this seems to be the best paying one at the moment.
As far as a money market, some banks require a minimum $2500-50000 deposit to start earning interest. Interest rates are running on par with the youth CDs so there's really no advantage going that direction.
There's also savings bonds. I bonds are really popular right now since they follow inflation and can be cashed in as less as a year. Here's another article from the US Treasury that explains how bonds work and pay out:
http://www.treasurydirect.gov/indiv/research/indepth/ebonds/res_e_bonds_eecomparison.htm
You really have several options when it comes to investing. If your parents have an accountant, he would be a good person to talk to about other investment options.