Monitors are meant for PCs = for Text, therefore higher resolutions are always favored. On the other hand videos will look good at 720p on small TVs (difference between 720 and 1080 is barely noticeable from a distance on a TV less than 30"), afterall standard TV and DVD resolution is only 480i/576i.
@itachi183, to add to what phoenixfx said, keep in mind that "720p" is only 1280x720. That low of a resolution isn't good for >20" computer monitor. Since the typical computer users sits 1'-2' from a monitor (compared to 10'+ for a TV) it's important to have a high resolution to keep the text clear.
Plus, most widescreen computer monitors are 16:10 aspect ratio, where as the 720p and 1080p resolutions are 16:9 (and hence HDTV's are 16:9), but that's another discussion.
I agree with HenryBravo. It's all about: 1) how far away your head is from the screen, and 2) what you use it for.
Monitors are expected to be 2 to 3 feet from your head. TVs are expected to be no less than 5 feet, and more likely 10 feet or more from your head.
Monitors need to show text almost all the time. TVs show moving pictures almost all the time.
People who try to use TVs for monitors often find text to be horribly unreadable. TVs are also tuned to do sharpening and artifact removal which wreaks havoc on PC gaming, doing more or less the exact opposite of what you want to do to make the game look better.
See this thread for first-hand descriptions of what makes most LCD TVs terrible choices for monitors. There may be some that aren't terrible, but you'll want to do a lot of research first; start here and here.