Sorry if this sounds obvious, but I keep games until I'm done with them.
Sometimes I'll realize that I'm not playing one of my games as much and that I've done everything I can with it. I still love R&B and Junk Yard, but after about 2 years the time came for them to move on to new homes.
Sometimes I get a game and discover that it's not a match for my tastes and it's not as enjoyable as I'd hoped. That was the case with POTC, which I had for about six months.
One time, I bought a cheap game intending to flip it - I fixed it up and sold it for a small profit after about 12 weeks, but I wish I had kept that one a little longer. My only regret.
Otherwise, I buy all my games with the attitude that I'll get joy out of them for as long as I can and move them on when their time comes. My longest-lasting game has been with me for seven years.