It really depends on the movie, and how well the remake is handled. One of my favorite movies is the Ocean's 11
remake. It's just so much damn fun to watch!
The problem is: if the original is good, then the remake has a lot to live up to and it can be hard to do that (though it does happen). But if the original is bad, the remake will have an easier time. Also, a lot depends on how much changes bother you. To me, getting irritated over changes usually isn't worth the headache, so long as a film still stands fine on its own. Heck, sometimes changes can be for the better.