There is only a difference when the output of the signal is greater than 720p. Blu-ray, HD cable channels, and PS3 are usually the ways in which people achieve 720p+ output. Generally, standard cable output is somewhere around 500-600p - it doesn't even take advantage of the 720 pixels you already have - but sometimes (as in the case of sporting events), broadcasters will choose to show the program in hi-definition. When this happens, there is a definite difference in clarity.

If I were to compare it to having a digital camera, it's similar to going from a 4MP camera to a 7.1MP camera. The same picture taken with both cameras will show that one has more detail (because of the increased pixels) and holds its integrity as you enlarge the photo. Another way to think of the difference is to think back to the difference between VHS and DVD quality.

Keep in mind that although the program may be broadcast in high definition, the commercials may still be broadcasting in standard definition (SD) and will shrink to a smaller size on your television when they air. This causes the black lines to thicken on the sides of your television to compensate for the lack of usage and is completely normal.

My recommendation: 1080p is nice to have if you use it. It can add a lot to your viewing experience. If you don't intend to watch movies in High-Definition via Blu-ray or HD channels, 1080p might not benefit you. I don't subscribe to cable, however, I'm still able to watch several shows which are broadcast in HD via a digital antenna.