I have to actively force myself to play games outside a core handful I always play. The reason for this is that most of the games I'm really into are pretty freeform and open-ended, like strategy games such as Crusader Kings 2, so there's really as much replayability as a person desires in them. To actually exhaust all possible options in a game like that would take, I dunno, decades? Then again I've been playing Civ IV for a decade and I'm still a novice scrub.

Similarly, some games do have pretty firm endings or definable end-states, but they're almost zenlike in nature so the replayability is basically "as long as I want it to be". A great example of this is Dynasty Warriors 8 (which is incidentally the best game in the series since 3 or 4) where I'm committing Wu/Wei/Shu genocide over and over and over, and it doesn't really get any less fun because it's just a solid stupid action game. Probably I'll exhaust the possibilities at some point, but it'll take awhile to get there.

When it comes to games with much firmer endings, whether I replay really depends on my mood. I imagine I'll replay some games - the Suikodens, Breath of Fires, some FFs - now and then for as long as I'm playing games. Some I finish once and put aside fairly confident I'm not going to go back to it. Bolivar was spot on when he said games should be appreciated rather than consumed, and when a game has merits* for an individual, that appreciation might be something close to timeless. Then again, vidya isn't much older than the older members of the forum, so who knows how this will play out when the medium is as old as movies are today?

* I say "has merits" rather than "is good" because I know in my own case there are games I've enjoyed which I can't really argue are actually good, they're just personally enjoyable. Conversely there are games I recognize are excellent but which do nothing for me.