I offer recommendations that will likely not be mentioned by anyone else:
Ah! My Goddess!: The harem anime version of Bewitched!
Watch if you want to laugh and say Awww!
every once in a while.
Daphne In The Brilliant Blue: The Perfect Anime! Yes, I mean that! THE! PERFECT! ANIME! Literally one-stop shopping for everything you could ever possibly want in an anime! A sci-fi storyline, comedy, drama, mystery, gunfights, chases, ridiculous amounts of fanservice, gender-bending, cosplay! A must watch!
Starship Operators: A slow-starting storyline but some of the best space battles I've ever seen.
ARIA: I barely know how to explain this one. It's like...chamomile tea. I'm generally an impatient, easily bored person, but I watched this series and it has like a scary calming effect. Nothing happens. Literally nothing, but you don't care because it's just so overwhelmingly nice it hypnotizes you into watching every episode.
Um, anywho, it's about Mars being turned into a water planet and there's a copy of Venice and its the story of the gondola pilots who are cute girl students.
Yeah, I know, but I'm telling you it's hypnotic!
Gunslinger Girl: Before I watched this I wouldn't have thought it possible to feel sorry for almost every single character in a series. This show is deep and sad as well as violent, but fantastic.