Could you please explain why non-HDTV programming (air, cable or DVD) looks worse on HDTV's than on a regular CRT?The answer lies in the nature of flat-panel technology (e.g. LCDs/Plasma). Images on LCDs and plasmas are made up of small dots that are fixed on the screen called pixels. The number of pixels on those TVs are indicated by the native resolution of the TV - usually it is 1366x768 on most LCDs and Plasmas (these are called 720p models), 1920x1080 on higher LCDs and Plasmas (these are called 1080p models), and on sometimes you get weird TVs that have wacky resolutions like Hitachi's 1024x1080, or 42" plasma's 1024x768. Generally the more pixels on the screen, the better the image is, depending on the brand of the TV of course.
Basic cable channels run on 480i signals, which means that it only has 480 lines of video resolution. Now HDTVs have at least 768 lines of resolution. Try to think of a 480i signal as a 4x6 picture and the HDTV as a 8x10 frame - the picture simply wont fit not only because it is too small, but because the 4x6 picture isn't the same proportion to the 8x10 frame! The only way to fit that 4x6 picture onto the frame is to blow the picture up so that it becomes a the same size of the 8x10 frame. The processing in which the 4x6 picture becomes a 8x10 will only seek to make the image worse (how can you possibly make a blown-up version of a 4x6 picture look as good as the original....the answer is you can't. That's why cable programming looks bad on HDTVs.
So if you are feeding your TV a small resolution signal (e.g. 480i from basic cable, or 480p from a progressive scan DVD player), the image won't look that great. If you feed it a signal that is close to its native resolution of 720p or 1080p, e.g. 720p or 1080i signals, then it will look fine.
That answers why basic cable looks like crap on HD sets. Now to the reason basic cable can still look good on a tube. A tube TV has a series of ray guns in its back that provides you with the picture you see on the screen. The screen on the tube TVs don't have fixed, physical pixels on it. In fact, the tube TV ray guns can display exactly what you feed it. For example, if you feed your tube a 480i basic cable channel, it will display all 480 lines without having to blow up the image to fit 768 lines like an HDTV. This is a rather crude explanation, but I'm sure you can find a better one on Cnet.com. One way to think of it is that a tube playing basic cable is using a magnifying glass to blow up an image; there is practically no distortion. On the other hand, if you try to blow it up with an HDTV, think of yourself copying and pasting the same image from before onto MS Word and dragging the arrows to make the image bigger, it simply looks bad. Both can blow an image up to a certain size, it's just that tubes can do them better than flat-panels.
720p vs 1080p, which one should I get?If you had to choose between name-brand 720p or budget brand 1080p HDTV, I’d go for the name-brand TV. Things like contrast ratio and overall picture should be the deciding factor, not simply just the pixel count. You are going to have friends who will tell you otherwise but it's peer influence coming from ignorant people make the average person make sometimes not-so-wise decisions. The benefits of 1080p are usually only noticed when you are sitting close to the screen and/or when the television is big (50"+).