I got 2 chipped boxes and there is so much that you can do with them. Microsoft really missed the boat on this one they should have allowed PVR and media center capabilitys like the PSX is going to do.
Yes you can get it to play illegal copies of games but I use mine for playing movies mostly. I archive a lot of TV onto my server and I can use my xbox to play it back. My Replay TV device can only hold 40 hours so I move shows to my server. Once I move them off the ReplayTV I can't play them anymore with it so I have to watch them on a computer or my xbox. With the xbox I have a simple way to get a high quality picture and sound on the tv.
I replaced the hard drive in my xbox. Now when I go up to the cabin on the weekends I FTP a bunch of movies to it and play them with a projector for the whole family. Its a great time!
My other favorite thing is to copy my games to the hard drive so that I can leave the disks at home when I travel. I've just started to get into emulators and am having a good time exploring all the different systems I can play on it.
EDIT-
How does it work and in wich format are the copies burned!?
Back on topic- The chip allows you to load unsigned code. Unsigned code would include homebrewed programs like media players, emulators, ports of old games like quake and duke nukem. Backups of retail games are also unsigned since no one has found a way to hack the digital signature they simply strip off the check for it instead. It also allows you to load several different versions of Linux which will almost give you the functionality of a real PC. Personally I think running linux on an xbox is a waste of time but some people like to do it just because they can.
Xbox DVD's read from the outside in, which is why a standard PC drive can't recognize them. Most xbox's will recognize cdrw's and dvd-r. Some will recognize dvd+r and even fewer will recognize cdr. If you don't have a dvd burner you won't be able to back up most games but you can copy them to the xbox hard drive, at least untill you run out of room. Xboxes have a 10gb hard drive in them. They come formatted to 8gb but accessing that extra 2 gig is really easy.