It depends. When the MGS HD Collection released, I was all over it. Aside from me being a Metal Gear fanboy, it was enticing mainly because of the opportunity to finally play Peace Walker (didn't have a PSP), and the performance upgrades the games received (MGS3 at 60 fps? Yes please). And the art book that came with the collection was a nice bonus.
With Resident Evil HD, I don't know what was changed or upgraded besides the resolution and controls. And I still play on 4:3 and use the original tank controls. So, there's not much that really changed, but I still purchased it because I love the game regardless and I don't regret it one bit.
On the other hand, there are some remasters I absolutely will not consider, like the Silent Hill HD collection. Barring the numerous technical issues, Konami saw fit to redo the voice acting, which is a big no no in my book.
So, I guess it juat depends on what game is being remastered and if I really want to play it again.
For Silent Hill 2, you could change between the new and old voice acting. For Silent Hill 3, you had to listen to the new voice acting.
Again, it's probably a small thing compared to the numerous technical issues, but it's a matter of principle to me.