1) Because of nostalgia. Reliving our youth or the "good old days" or remembering how much fun you had playing them when they were new!
2) Run well. Typically your new games require fast expensive, new PC's or consoles to run. Old games tend to run much better and you can max them out and not worry about not being fast enough. Granted, some old old games are tricky to configure with modern hardware, but there are almost always ways of doing it. Even on modern systems old games can sometimes run better and look better than they did in the old days! (take emulated games for example!). And when a new game comes out, it often needs patches or revisions or mods before it becomes truly "playable" for most people. An old game is "finished" and "complete" and so you don't need to worry about it. All the cheats are known, so you can skip right to the part you like!
3) Because gameplay is king! New games may have new graphics, but many old classics are still fun to play.
4) Simpler games from a simpler time. Now granted, this is not all games. There are plenty of old games that are complex and new games that are simple. But for some, many of the older arcadey games are a lot more relaxing to sit down and play, rather than having to spend hours and hours and hours on a game quick saving constantly to make it through, then feeling like you had to do WORK instead of having fun!
5) Old games tend to be cheaper.
Not always, but again, new games cost a lot, older games usually less so. So they don't break the bank if you want some fun! Especially nowadays with new games that are high on graphics, but often lower on replay value.
So there you go. Today's "new" games are tomorrow's "old games." Each to his own... and it's all a matter of taste in the end.