Happy to see this works different for everyone. Replayability in games is something I can crap on about till the sun don't shine, but I'll point out the factors that stand out to me (with examples, hooray!)
- Simply solid controls/mechanics/balance/feel
[Counter-strike, Rainbow 6 Vegas 2, Killing Floor(s)]. Good controls, nice sounding and kicking guns, solid reload animations, nice competitive balance, difficult but tactical play rewarded. Really all there is to it, just a joy to play.
- Branching story line
[KotOR, Mass Effect, Bioshock] So you want to see what happens if you go with the other guy. Or if you make all the different moral choices and go extreme good/bad. Or just to get the different ending.
- Variable play styles
[Witcher, Borderlands, almost any RPG] Just want to try a different way of hacking or burning enemies up. Magic instead of swords. Maybe two swords. Maybe stealth. Maybe guns that shoot acid. Whatever.
- Just a short, good ol' romp
[Most arcade emulators] Fighting games emulators, especially Streets of Rage. Always a soft spot in my heart.
And any combination of the above!