About a year ago (when I was still on the robotics team) I got a good work assignment; build and program a lego robot for a sumo competition event (picture on the right). That was fun, but I forgot about the fun for a while. until a few weeks ago when a new collegue on my current team asked for advice on what to buy for his eleven year old son that was interested in robotics and wanted to do something.
There are several options out there for the robotics hobbyist but if you're young (or old) I think Lego is one of the best options to start out. Lego is always fun! And it's compatible with your other Legos! It also have both a simple way of programming your robot using the Lego NXT software or you could just use bluetooth and whatever programming language you like!
There is also another thing you should know if you consider getting a Lego Mindstorm kit. Don't go down to your local store and buy a kit. There is a site not so known where you can get great kits for a little less money: Lego Education. The base set and the education resource set gives you a very nice base to start with (that is what I used for the robot in the picture and I did not use all parts).
If you want more inspiration, you can always watch this video: