Depends on what games. With the Gen 3 games, I unfortunately found myself only playing them once. I'm just not really into those games like everyone else is, but I don't not like them or anything. I'm just weird. xD
With games that have a nostalgic value i.e. Platinum and Diamond in my case, I'd want to play them a lot since every play through I could play the game differently or something like that. I also like to remember the old days when I just got the games when I replay them for some reason, again nostalgia. Or if it's a game I like i.e. Gold and Crystal, I'd replay them as much as I can before getting bored, which is around 2-3 replays.
The newer games to me don't have as much replay value as I don't find them as interesting, neither do the first generation and their remakes. I don't know, there's just something that turns me away from the 1st gen games and their remakes...