It entirely depends. If it's a long RPG I may linger an extra few hours to do some side missions I didn't finish or explore a little more. If I ever replay it,usually months or years down the line. Sometimes on a different platform. If the same copy of the game usually only if it has NG+
Stylish action like a DMC/Bayo or anything in that genre. Short games. I replay my fave stages right away.
TPS is like VanQuish/Gears, and others like it. I can start over and play to the point I want, stop, and start again. Same can apply to any FPS I like.
Some games I just use a chapter select and replay a chapter or two.
Ratchet and Clank games I replayed them right away. Short and with keeping my upgrades it goes faster.
Something like Shenmue is special to me, where I finished the game many times in the past but now I will start a new save and just get to a certain point and asorb the world for a while, then put it down. Repeat the process some time later.
Some older games I once replayed a lot like a Sonic Adventure or SM64. I just don't anymore as I feel I only have a few years left as is, so looking for new experiences and some of the games I played a million times from my youth need to take a backseat. Time is short.