I am by no means an expert on the subject but I know how emulation works. I wanted to write this as a topic that could be pinned for newcomers to read before they start asking for PS2, Gamecube, and DC emulators.
Every system has it's own unique and different hardware. And each system has it's own individual coding methods and SDKs. So obviously you can't just play a PS2 game on the XBox and so on. Because the coding is different and written for a different set of hardware.
What an emulator does is recreates the specific hardware for another system with software. And then that software runs on the hardware of the host system. So just imagine for a second. Two systems that are just about on par with each other as far as speed goes. The only way to get full speed would be to have the true hardware for the system. Software could never hope to emulate a system that is close to the same speed as the host hardware. For a good example, think of hardware rendering vs software rendering...which is faster? The hardware of course.
Another way to think of it is when you put a game in your PS2, the game just runs right off the hardware. If you were trying to emulate it on the XBox, first it would go into the software and have it's code and commands changed to the native language of the XBox, and then that new code would be run. And being that the systems are so closely matched in speed, the emulation would be very, very, very unplayably slow. And the problem with PS2 emulation is there really isn't even a working one for the PC yet.
Now why can older systems be emulated? Because compared to a PS2, their hardware is very simple to manage with an emulator. The XBox can manage the code fast enough to keep the game going at a steady clip. I know this isn't an in depth explanation, but I thought I would put it in laymen's terms.
Basically...here is the gist of what I just said...PS2, Dreamcast, and especially Gamecube emulation is not going to happen on the XBox. It just can't handle it. Granted one could be made, but it would be so slow and ugly it wouldn't even be worth the effort.
Anyways...case closed...after reading this there should be no reason for anyone to ask questions about why PS2 emulation can't be done.