Accio is the summoning charm. It can be used in two ways: casting the spell and then saying the item that is to be summoned, or by pointing the wand at the object and casting the spell. It's opposite is Depulso, the banishing charm (see below).
Aguamenti causes a stream of water to shoot from the caster's wand. For example, if a fire starts, the wizard or witch can cast Aquamenti to put out the fire.
Alohomora can be used to unlock and open doors. It can open doors that were sealed with the Colloportus (see below) spell.
Anapneo clears a person's throat, if blocked. It is a useful substitute to the Heimlich maneuver.
Aparecium makes invisible ink and other invisible items appear.
Avada Kedavra is the killing curse and is one of Unforgivable Curses. The spell creates a burst of green light and kills the target immediately.
Avis makes a group of birds fly from the caster's wand.
The Bat-Bogey Hex causes bogies (or boogers in American slang) to change into bats that can be used to attack.
The bubble-head charm creates a bubble to appear around the caster's head. Can be used as a breathing set.