Accio
This spell can attract an object to the caster. The necessary incantation is "Accio" which is usually supplemented by the spell's target (for example, to summon a broom, one usually needs to say "Accio broom"). The wizard also needs to concentrate hard on the object he is trying to Summon. Knowing the general location of the object is essential, also. "Accio" (from "accire") is Latin and means "I call/summon". First seen in Harry Potter and the Goblet of Fire.
The opposite of the Summoning Charm is the Banishing Charm (incantation unknown) which is supposed to repel an object away from the caster.
Alohomora
This spell is used to open a locked door or window. Pointing a wand at a door and saying "Alohomora" will unlock the door. This spell can also open doors which have been magically sealed with the Colloportus spell. Doors can be magically sealed with sufficiently advanced spells so that Alohomora cannot open them, such as the door in the flying key room in Harry Potter and the Philosopher's Stone.
Aparecium
This spell makes invisible ink and perhaps invisible items in general appear. First used in Harry Potter and the Chamber of Secrets when Hermione tried to make something appear in Tom Riddle's diary. From Latin appareo, which means "I appear."
Avis
Makes birds fly out of the wand of the spellcaster. Used in Harry Potter and the Goblet of Fire by Mr. Ollivander to test Viktor Krum's wand. "Avis" is a Latin noun (nominative, feminine, singular of the third declension) meaning "bird".
Cheering Charm
Incantation unknown. Causes the person whom the spell was cast upon to become happy and contented, though heavy-handedness with the spell may cause the person to break into an uncontrollable laughing fit. Invented by Felix Summerbee (1447-1508). First seen in Harry Potter and the Prisoner of Azkaban.
Colloportus
This spell can magically lock a door, preventing it from being opened for a presumably limited amount of time. It is easily countered by Alohomora, however. The word is a combination of "colligere" (Latin for "bind together") and "portus" (Latin for "door"). Used in Harry Potter and the Order of the Phoenix when Hermione needs to seal a door in the Department of Mysteries against some Death Eaters.
Confundus Charm
The Confundus Charm is a confusion spell. The word is derived from the Latin "confundere", to perplex. [1] (http://www.hp-lexicon.org/magic/spells_c.html) First seen in Harry Potter and the Prisoner of Azkaban, when Professor Snape suggests that Harry and Hermione have been "Confunded" so that they will believe Sirius Black's claim to innocence.
Deletrius
Gets rid of spell echoes caused by Priori Incantatem. First seen in Harry Potter and the Goblet of Fire when Amos Diggory gets rid of the echo of the Dark Mark from Harry's wand.
Densaugeo
Makes the victim's teeth grow rapidly. Introduced in Harry Potter and the Goblet of Fire when Draco Malfoy attacked Hermione outside of the Potions classroom. "Dens" is a Latin noun (nominative, singular, masculine of the third declension) and means "a tooth". "Augeo" is a Latin verb (first person, active indicative of the second conjugation) and means "I grow" (from the infinitive "augere" which means "to grow").
Diffindo
Rips something apart. Used in Harry Potter and the Goblet of Fire when Harry urgently wants to talk to Cedric Diggory and casts this spell to rip his bag, thus delaying him for class.
Dissendium
Causes the humpbacked witch hiding the secret passage to Honeydukes to open up. First seen in Harry Potter and the Prisoner of Azkaban.