Remakes are largely bullshit, I just want the classics updated so they run smoother and look better while keeping the same art style and feel. Sometimes the controls can be updated as long as we get multiple options (no one wants N64 or PS fps' with the old single analog control schemes alone).
Like the Nightdive Studios versions of classic games are a great example of what I'm talking about. They care a lot about giving you the classics just in higher framerates, rendered in hd, with tons of options. Same with Metroid Prime or Windwaker's HD versions (they got updates that stick with the original look very strictly, gameplay changes were largely just making things a bit smoother in certain aspects like being able to get the quick sail earlier in Wind Waker).
I think the old school 2-D Final Fantasies (especially IV and VI) and Chrono Trigger would work great in Square-Enix' hd-2d art style they have been using lately, but I don't want to see them get fully 3-D remakes.
All that being said number 1 for me is the Timesplitters trilogy.