Keyboard instruments in other temperaments (for example some Baroque tunings) may split the black keys (for example) into separate sharp and notes; sharps are used for sharp keys and flats for flat keys.
Choirs and instrumentalists who can dynamically adjust the pitch of individual notes will often do so for better tuning. (Some software instruments can also adjust tuning dynamically as you play.)
Many (if not most) pieces of music (perhaps most famously Bach's Well-Tempered Clavier) were composed with a particular temperament in mind.