For the unitiated, here's a glossary of the words you'll encounter below:

biseinen: "beautiful youth" (male, usually in twenties)
bishoujo: "pretty girl" (teens)
bishounen: "pretty boy" (teens)
fanservice: underwear shots (or just plain old female nudity) to satisfy the typical male anime audience.
Gainax: a well-known anime company that puts out the most bizarre animation you'll ever see. They made their name with Neon Genesis Evangelion, but somehow they're always in financial trouble.
mecha: giant robot (mechanical), occasionally partly organic, sometimes sentient.
shoujo: girl; shoujo anime is usually romance-oriented and filled with bishounen.
shoujo-ai: girl-girl love, usually very cutesy and innocent.
shounen: boy; shounen anime is usually action-oriented with a good dose of fanservice.
shounen-ai: boy-boy love, usually limited to hugs and kisses.

FLCL (Furi Kuri)
keywords: Gainax, fanservice, insanity, sexual innuendos, action, crazy science fiction, anime on acid
description: A young boy is hit on the head by a motorcycle driven by an alien. Any more would spoil it.

Grave of the Fireflies
keywords: drama, angst
description: A boy and his sister try to survive after their home is destroyed by firebombing during WWII.

Gravitation
keywords: shounen-ai, beshounen, biseinen, comedy, drama, angst
description: Cute singer of a new rock band falls for a popular novelist.

Neon Genesis Evangelion
keywords: Gainax, angst, mindfuck, angst, drama, angst, action, angst, comedy, angst, fanservice, angst, and angst
description: Depressing and philosophical plot starring mechas and teenagers in skin-tight suits.

Noir
keywords: action, drama, angst, bishoujo, between-the-lines shoujo-ai
description: A deadly young girl with amnesia joins a top female assassin to fight a mysterious organization.

Revolutionary Girl Utena
keywords: shoujo-ai, bishoujo, bishounen
description: Crossdressing girl duels to protect the "Rose Bride." Sort of.

Trigun
keywords: comedy, angst, action, drama
description: Western-style anime set in the future on a desert planet.

The Vision of Escaflowne
keywords: fantasy, drama, action, angst, romance, bishounen, biseinen, bishoujo, non Mary Sue female lead
description: A girl from Japan with a mysteriously accurate talent at fortune-telling is sucked into another world.