Proper remakes - that is, re-releases with additional content - I will buy most of the time if I enjoyed the original. It depends on what the new content is, as well, and how much of it there is; if I'm going to be paying for the same game again, I like to get my money's worth. A graphical overhaul and maybe a couple of extra costumes or additional scenario or whatever, if I've played the game before, just won't cut it for me if the game wasn't that exceptional to begin with.
Remasters, which are essentially the same game with a shiny new coat of paint...not so much. Really it depends on the system for me, and how recently it's been since I've played the game. As an example, I played OOT on the Gamecube, and I can easily put the disc into my Wii, so I avoided the 3DS remaster; it didn't offer anything substantial for me that I hadn't already seen before. But it's been several years since I played FFX and X-2, and digging up my PS2 would be a royal nuisance, so the second the remasters get released (if they ever do...) I'll be all over them.
I do wish that companies would use remasters and remakes as a way of making their lesser known or harder to find titles more readily available, though, rather than as cash cows. Games like God of War and The Legend of Zelda don't really need HD remasters - they're everywhere. You can buy a second-hand console and the game for about the same price as the remaster if you go to the right place. Titles like Zone of the Enders and ICO/Shadow of the Colossus, which are hard to find and/or painfully expensive, however, definitely benefit from the treatment, because I know I'd never pay more than retail price for a game several years old, no matter how good it is.