I have an nVidia GeForce 5700 card with DVI output and a Sanyo HD CRT TV with DVI input. The caveat is that the DVI input is "not for use with computer."
What this means is that regardless of what resolution the xserver is set at, the TV always overscans HORRIBLY leave the top, bottom, left and right non-visible. I'm pretty sure I could use S-Video or Composite, but DVI looks much much crisper on this display and I'm already using those other inputs.
When I had MythTV installed on this box I was able to set a GUI size and position option in the MythTV config. This allowed me to set the resolution to 800x600, which seems to look the best, and then set the size and position so my GUI filled the screen perfectly. MythTV also allowed me to specify the commandline passed to mplayer, and I was able to add options to the same effect.
Is it possible to do these things with LinuxMCE? Also, do the newer graphics cards support DVI compatible with TVs, or are the newer TVs just accepting standard PC display resolutions?