Anime is cool stuff and I watch a lot of it, but you gotta know what kind you like or you'll just end up watching something perverted or girly (not that it's bad)... I have watched a few anime about love and relationship stuff. But seriously, if you know what kind of shows you like there's probably an amine for it. Also It depends on how long your willing to watch a show. Some of the series can run up to 200+ episodes while other are only 6 episodes long.
There's a movie called Cencoroll that is a wicked anime movie, and it's only 30 minutes long. If you don't know what animme is all about I suggest you watch this short masterpiece. It's everything that an anime should be (kind of like pokemon lol)
For the music lovers there's Beck and Detroit Metal City, and for the Action lovers there's DBZ, Naruto, Bleach,
If you like samurai then check out Samurai Champloo, Samurai 7, Afro Samurai and many others.
try Tokko or 11Eyes if your into monsters
True Tears is a good love story and so is Lunar Legends (it's more about the action/fighting though)
Some awesome movies would be Akira, Tales of Earthsea, Perfect Blue, and Princess Mononoke.
an for something a little different try Airgear, Bakemonogatari, Wolf's Rain and Higurashi no Naku Koro ni =P
http://www.animespree.com/category/higurashi-no-naku-koro-ni/