Play it and you can come back and agree with me. The original is garbage compared to it. I have both games. I deleted the original off my PS3 hard drive now that I have the remake, it's somewhat cool for nostolgic purposes but it doesn't make me feel any interested to play it seriously.  It's easily the biggest case where a remake makes improvements over the original. I'd rank the remake up there with my favorite games of all time.

Tomb raider II and III

Halo 2

Banjo Kazooie
Donkey Kong 64
The original Luigi's Mansion
Breath of Fire 3
Mayyybee... Metroid Fusion.

Suikoden 1
Suikoden 2
Final Fantasy 6
Final Fantasy 7
Final Fantasy X

And a side order of Xenogears! =D

Metal Gear
Metal Gear 2

MGS can stay how it is.

1. Chrono Trigger
2. Super Mario 64
3. Donkey Kong 64
All I can think of at the moment. I loved all of these games, but it'd be cool to see what they'd look like using current technology.

EDIT: Completely forgot Majora's Mask! Would love to see a remake of that as well.

1. Super Mario RPG

2. Chrono Trigger

3. ...............................

3..........

hm....

I guess... OH

3. Mario Party 2

4. Mario Kart 64

5. Final Fantasy VI

I like you style, but no Chrono Trigger?

Hmm....this is a tough question. Usually I prefer remakes to arrive at least ten years after the original game -- although the Resident Evil remake and The Twin Snakes are obvious (and successful) exceptions to that rule. And, ideally, the original game would have been less-than-stellar to begin with, so that a remake would have room to improve.

So I'll go with these:

1. Zelda II: The Adventure of Link
2. Castlevania II: Simon's Quest
3. Battletoads
4. Quake
5. Resident Evil 2