For me a big part of it is reliving the games I grew up with, or feeling the nostaliga of the era, even if I am playing retro games I never played back in the day. I also like the simplicity of older games. With free time constantly dwindling I grow tired of load times, waiting for games to install to the hard drive and downloading updates, conenctivity issues and lag for online games, etc. Nothing quite like putting in a game cartridge, clicking "on" and then starting the game within seconds.
I love the collectibility of older games too. I love the box art, the manuals, the maps that came with some games, I love the care that went into the whole package of a game back then. Now, you get a disc/cartridge and an otherwise empty case. Feels half-assed to me. Also, many games of today feel like the same damn game over and over. How many Call of Dutys, Maddens, Grand Theft Autos, Far Crys, Halos, etc do we need? I'm tired of online required games as other players often ruin the game for me. There are new games I enjoy still but many of them are retro in style, like Shovel Knight, or sequels to long loved classic franchises like Zelda or Mario. Retro games just have so much more personality than most new games too.
One last draw of retro games too is the fact that they're all avialable. There is no waiting for release dates, no pre-ordering, being hyped for something that ends up disappointing. The entire libraries of all retro systems are out, with reviews for pretty much every game, so you can pick and choose which ones you like.
Edit: And one more reason i thought of is that most modern games lack both replayability and challenge. Sure there are games like Dark Souls that really test your patience but most games are too cinematic and full of cutscenes and not enough actually gameplay.