The Xbox is a sixth-generation console released by Microsoft in 2001. Known originally as the DirectXbox, this console is notable for essentially being a PC, as a result of using components from both Intel and Nvidia as well as being x86-based. It is the most powerful console from the sixth generation.
Cxbx can boot around 61 games, with around a dozen in a playable state (List)
XQEMU is an LLE emulator which is gradually advancing. As of now, it can emulate the BIOS and many games at very slow speeds.
Xeon can emulate Halo CE to the point where the first stage is semi-playable. The walls and ground are pitch black and the game crashes after you complete first stage (or right after you select the difficulty on modern versions of Windows.)
The Xbox 360 is backwards compatible, but it is not fully accurate. While some games work off the bat, many need patches downloaded to play properly. This requires one's Xbox 360 to have system storage. Even then there are still issues with many games from graphical glitches and slowdown to errors that can make gameplay impossible.
The pratfalls of Xbox emulation
Due to a lack of interest, a lack of console-exclusive games, or in some case very toxic behavior or potential legal threats towards developers, the Xbox emulation scene has remained dormant until recently. For the projects currently available, there is a high barrier to entry for the effort involved. In spite of its very PC-like hardware, the Xbox has enough proprietary elements to make emulation non-trivial. Many aspects of the Xbox's CPU, GPU, audio and BIOS are undocumented and not fully understood.