One thing I've noticed on DVD is that the picture is noticeably squished together and when it is put on Blu-Ray the proportions become more natural with drastically better skin tone. Those Amadeus comparisons prove just how dramatically DVD is squished together from its original film source (everyone looks much skinnier on DVD than on Blu-Ray).
Granted, this is an example of videotape footage that is pretty much ancient, but look no further than Elvis' '68 Comeback Special (besides being tinted a horrible orange color that wasn't on its previous releases). If you put that video on your computer, it looks like it's completely at the wrong width. Elvis has a long face, but never *that* long. I remember when people would post screen caps from the DVD, it just never looked right proportionately, and you'd be seriously tempted to go into Photoshop and try to make it look a little more realistic.
I mean, this is shockingly distorted:
http://img13.imageshack.us/img13/7978/6820leather2046.jpg
DVD screencaps are often horrible to look at next to photographs, while film stills from a better source can look like photography.
There was another DVD/Blu-Ray comparison site I found where they had Terminator 2 as an example--and that one was REALLY dramatic (as in: the DVD was squished beyond human proportions and the Blu-Ray corrected it). You can also see this effect on that above Amadeus comparison link--check out the two images of Jeffrey Jones as Emperor Joseph II. The head proportions are, once again, squished and too red with grainy eyes vs. the image spread out more and the color corrected and more detailed.
Overall, on your analog T.V. you're not going to notice much at all. Even a smallish HD screen still plays DVDs that look just fine and barely different (though the bigger the HD screen, the more noticeable the quality change gets). The real test of quality is if you get into screencaps on your computer, then you realize just how dramatic the Blu-Ray upgrade is.