I use mutes very often during practicing out of courtesy to my neighbors, however I find that certain mutes seem to work with certain songs or styles better than others.
Harmon mute: blues and just about any ballad.
Straight mute: those classical, patriotic or European style songs.
Solotone: nostalgic type songs like dixieland or folk ballads.
Cup mute: hard bop, I can't figure out exactly why, maybe Dizzie liked it, but the cup seems to have better articulations than the harmon.
Bucket mute: Ballads that I would play quietly anyway, but I want to tone down the airiness.
Plunger mute: ?? I don't know that well, but it seems to work when I want a funky style or with songs with varied dynamics.
Practice mute: practice early in the morning.
When do you use your mutes?