You can almost always reach somebody famous through the place they work for. Bands have record labels. Writers have publishers. Athletes play for a particular team. Look on the jacket of the CD, the box of the video or the inner page of a book.
Official websites are also a good place to find addresses.
You can find lots of listings by typing in the name of your favorite star at the Yahooligans website. Here are a few addresses I dug up for you from different places. Be sure to write the name of the show and the stars name on the outside of your envelope. Collecting letters from celebs is a great hobby. Special thanks to Anneka , for sharing Leonardo's address and suggesting this article and Chris for editing it.