MCE 2005 requires at least a 1.6 GHz (or equivalent) processor, DirectX 9.0 hardware-accelerated GPU (such as a recent ATI Radeon X series or nVidia GeForce 6 series), and 256 MB of System RAM. Some functionality, such as Media Center Extender support, use of multiple tuners, or HDTV playback/recording carries higher system requirements.
Media Center is much more restricted in the range of hardware that it supports than most other software DVR solutions. Media Center tuners must have a standardized driver interface, and they must have hardware MPEG-2 encoders, closed caption support, and a number of other features. Media Center remote controls are standardized in terms of button labels and functionality, and, to a degree, general layout.
A TV Tuner card is not req'd, but if you want to use your PC to watch tv, then it is req'd