I thought it was Analog monitor but now I have a Widescreen LCD and they still look the same. When I look at the same websites with my CRT at work it's not as "grainy". Like for example Amazon.com, the pictures of things look really grainy??
Sounds like your widescreen LCD may not be at it's native resolution. This will make web graphics look especially bad as opposed to Window icons. Suggest you find out your monitor's native resolution and ensure that's what your screen settings are using.
To try to rule out or confirm your browser as the cause, you could try right-clicking a fairly large picture on a web page that you have trouble with, saving it to your hard drive, and then opening it with any other program besides your browser. You could then compare the pictures side-by-side.
Also, I discovered just a few months ago that LCDs often do not come factory default at very optimal display settings. If you have Media Center Edition, I suggest you open up Media Center and go to Settings -> General -> Media Center Setup -> Configure Your TV or Monitor. Just run through that and pay especially close attention to your LCD's contrast and brightness. If you don't have MCE, I'm sure you can find another good test pattern or something similar elsewhere, just not aware of any good ones off the top of my head.
Also, as Mark_Warner said, check your color depth, though that would affect everything and not just your browser.