In a completely biased and inexperienced view, I would recommend Soul Eater, Tengen Toppa Gurren Lagann, Death Note, maybe FLCL. I don't really know, my knowledge of anime is sadly pretty generic.

Panty & Stocking with Garterbelt is pretty awesome as well, but I wouldn't recommend it unless you have a very very very very clear idea of what you're getting into.

Some other good ones(note alot of them are Mecha):

Code Geass

Gundam 00

Genesis of Aquarion

Full Metal Alchemist

Full Metal Alchemist: Brotherhood

Darker than Black

Eureka Seven

I'll post more as I remember them.

Mobile Suit Gundam, Gundam Unicorn, and Gundam Wing are good too. Seed starts out kinda bland and ripoffish, but gets a bit better about halfway through the season. Then Seed Destiny kinda makes it bad again until Kira comes back as the main character halfway through.

it is impossible to not like Cowboy Bebop

Trigun. Samurai Champloo. FMA: Brotherhood.

I will always be an advocate of Death Note.

If you want other Anime fans to hate you, you could watch Naruto.

I .. dunno what to recommend since I'm not a huge fan of Anime either.

How I can say Gundam series are very good, specifically Wing, 00 and 08th MS Team (that's probably PG-13). But I like those series. The characters are realistic but it's not scary like some Anime can be.