Instants can be played throughout the play cycle. My gripe as a beginner is that Magic's play cycle is very difficult to understand....maybe I am destined to suck at Magic. During the RTR prerelease I was at such a loss!! Yes, I know: untap, draw, upkeep. That is what my kind opponent kept patiently saying. Anyways, if you leave some wiggle room in your mana pool you can play as many instants as your mana pool can bear at any time during play. The especially succesful instants force the player to play even more mana to undo the effect of the instant. Yes, Mana Leak, I am specifically referring to you!
My favorite instant these days is Tragic Slip.