J.S.
My youngest is 13. The two ideas she came up with when I asked her this question were a Minute to Win It party (this is what she is planning for her 14th in Feb.) or the photo safari party we did for her sister a few years back.
Minute to Win It is a sort of game show where the contestants have to accomplish some crazy thing in less than a minute. I think you can youtube some good ideas for that one.
The photo safari requires a non-rainy day, so it depends on when her b-day is. Can you count on a dry day? If so, this is what we did. We broke the kids up into teams of 3 or 4 and gave each team a digital camera (we have one, and we borrowed the other 3 from friends). We explained the boundaries of the safari (certain streets to create roughly a square area) and gave each team a list of 13 things to find (a house with the Christmas lights still up, an awesome car, an ugly old car, a dog, an animal not a cat or dog, a pretty garden, a house in need of a paint job, etc.) the list included two 'most' categories, most basketball hoops and most signs ( any kind of hoop or sign, but only one picture of each one you find. No duplicates) They had to have at least one member of their team in the photo and presentation counts! We gave them about an hour and a half to find everything on the list and get back to the house. When they returned we dished the cake and ice cream and then plugged the cameras, one by one, into the tv to view the photos. Some of the pictures were hilarious! Some were very artistic and creative. We had four teams and all the kids agreed on the overall winner. This was a few years ago and the kids still talk about it. It combined creativity and independence, but still was age appropriate.
Have fun!