I'll watch a remake if there's a reason to make the remake. For instance, being more faithful to the original source material, etc., or giving it an interesting spin. I also favor first class productions, rather than shameless money grabs. Similarly, American remakes of foreign movies can be cool.
Remakes I've liked: True Grit, 3:10 to Yuma, Casino Royale, Let Me In, Star Trek (a "reboot", rather than a remake), and probably a whole bunch more.