Flutes should pull a cloth through their instrument every time they finish playing.
Saxophone and Clarinet players should always have 2-3 good reeds. The reed should be stored in its case, not on the instrument. A cleaning swab should be pulled through the instrument every time they finish playing. Grease the cork(s) frequently to prevent them from drying out.
Trumpet, Baritone and Trombone players should empty their spit valve every time they finish playing. They should also oil their valves (trumpet and baritone) or slide (trombone) once a week.
Percussion players do not need to do any cleaning of their instrument but they do need to keep their cases neat and organized.