I don't really re-play games all that much simply because most of my favourite games are large time commitments. I often get a surge of nostalgia for something, but that doesn't always translate to me sitting down and replaying it again. There's just so much new stuff out there I want to try!
For me, it's definitely retro games that I like to replay, usually because they're short contained experiences. In particular, I love my Sega Saturn, and play NiGHTS and Panzer Dragoon on it frequently. I cannot get enough of those games. I also really enjoy playing Jet Set Radio on the Dreamcast from time to time. The aesthetic and soundtrack combined with the quick arcade gameplay makes it easy to pick up off and on.
Yume Nikki also gets an honourable mention here.
Pokémon (any version really, Platinum and Crystal are my go to games) is also always a solid game to come back to. Sometimes the real world gets me down, and escaping into a game in which most everything in the world seems right is uplifting. Plus, I associate Pokémon strongly with my childhood, so it always manages to make me really happy.