Last time we talked about streaming movies to the Wii directly from your computer, via wifi connection.
The Wii is not HD yet, and the connections are standard RCA jacks. You can have adapters for your PC or HDTV for cheap, but the resolution is limited to about DVD resolution of 480p, that of the Wii output.
The mplayer-ce can play almost any formats in any resolutions, but the Wii isn't fast enough for playing HD stuff. Down conversion from HD to SD is pretty intensive processing, decode HD stuff and then recode. You have to do it in your PC first. The processing takes roughly the same order of time as the movie play time, depending on your CPU.