When I have to name my favorite "old" composer, it has to be J.S. Bach. There are some simply sublime passages in so much of his music that it almost seems to lift the listener to heaven itself.
However much I could go on and on praising Bach's genius, it is rivaled by Mozart. One of the latest violin pieces I was given by my teacher is a piece by Mozart called "Table Music." It is written so that it is laid flat on a table (hence the name), with musicians standing on opposite sides. One musician plays the music looking at it from one side of the table, the other plays it while reading the music from the opposite side of the table. And it works. It all harmonizes perfectly. What kind of a mind was able to figure this type of thing out? I don't know if this is the only piece of its kind that Mozart wrote, nor if other composers tried their hand at it. Either way, it's pretty cool.
Here's a video demonstrating Mozart's "Table Music" featuring another young prodigy, such as Mozart was.