Totally depends on the genre. 10 - 20 fps are good enough for many games with fixed 2d backgrounds or slow gameplay: visual novel, point&click adventures, CRPGs, turn-based strategy, Layton puzzles...).
Solid 30 fps for are okay for games where speed and aiming aren't the focus: action-adventures, JRPGs, ARPGs, sport games...
For games where speed and accuracy are important (first-person-shooters, many platformers, many racing games, many multiplayer games...), 60 fps is mandatory, 90 - 144 fps even better.
VR games with head tracking of course need at least solid 90 fps. 60 fps with reprojection could be good enough too, haven't tried it yet.