It depends on your card, and the TV. Older TV's only support around 800*600, but newer TV's can support bigger resolutions, specially if they're HDTV Ready. The only video card that I know of that will support 16:9 (thats widescreen, btw) is the Radeon series (although I'm not sure as to which ones, I do know for sure that the 64 DDR will)
HDTVs can't use the same analog TV input signal. Many HDTVs just have a monitor attachment on the back, though, so TV-out is unnecesary. NTSC resolution is way less than 640*480 which is why even output at 640*480 looks like blurry crap. Definitely don't increase the resolution more than that!