I don't know about 'remakes' per se... but I've always been a fan of game series that were still in their early stages.
For example, I loved the Legend of Zelda series up until 'A Link to the Past' for the SNES (that was my favorite, though Ocarina of Time was not bad)... then the interest tapers off. Same with the Megaman series and Sega's Sonic series. Another facet of this is that these were the games I grew up with in the 80s and early 90s, so there are some good memories.
I think I'm just a sap for vintage gaming; today's games try too hard to seem 'real' in my opinion and I just don't find them fun. Plus I think that a series can only be milked so much before it gets tired.