Wha. . .? How can people be hating Sailor Moon? It's campy and cute, I love it. The manga isn't that bad either, but oh well maybe I'm just being a girl.
Vision of Escaflowne is really great, the series and movie are completely different, I recommend the series first. It's set in a future/past? world on the moon called Gaia and an Earth girl's struggles to return home. There is much action, comedy, magic and romance, all the good stuff.
Slayers is a good fantasy comedy and not to mention a classic. Lina Inverse is an anime staple everyoen should be familiar with.
Urusei Yatsura (Those Obnoxious Aliens) is the first series by Rumiko Takahashi (creator of Ranma 1/2, Inuyasha, Rumic World), it is also a classic, has many Japanese style word play jokes that require extensive footnotes to understand but helps overall in a person getting the jokes in other anime. It's about a perverted boy and the jealous alien princess who loves him.
Pet Shop of Horrors is really good, the stories are unrelated shorts, they are incredibly creepy and make me feel weird after watchign them.
Boogiepop Phantom is very mysterious and interesting, I've only seen about 5 episodes, want more.