Some people can really see a difference (or just say they can), some people see no difference at all or just don't care. It's not like the jump from VHS to DVD at all since that jump offered more than just quality (and a bigger jump in quality at that).
My TV is setup perfectly for my room (actually had a professional set it up which funny enough I had just about right on my own) and I can notice a small difference from DVD's to upscaled DVD's and BluRay and notice almost no difference in upscaled DVD's and BluRays. My wife can't tell the difference at all between the three.
If you have a PS3 and you can find BluRay movies at the same price or pretty close to DVD's, get the BluRay movies, otherwise, in my opinion it's not worth the extra money (usually more than $10-15 for a movie and a $30 difference for most series). If you don't have a PS3, I wouldn't fiddle with getting a stand alone player yet.
