My tastes will obviously differ from others but here we go-
Rahxephon- beautiful and unique mechs, great music, and a twisty turny story that will keep you guessing until the end.
STR.A.IN- Cool looking mechs …in space!
Gundam the 08th MS Team- Mechs in jungle warfare.
And if you really want to subject yourself to a taste of Evangelion I would suggest Evangelion 1.01, the story moves faster and there is far less whinning.
Black Lagoon- Awesome! Mezzo- Ditto! Gunslinger Girl- Pretty good so far… Baccano- Awesome series but hard to follow, the story jumps back and forth through time, and it has a HUGE cast of characters. Excellent voice work, good music, and exceptional animation. It also inculdes a supernatural element…
Cowboy Beebop- Cream of the crop. Armitage, Battle Angel, Cyber City are all pretty good.
Blood the last vampire (the original OVA)- It is gorgeous!!! Demon City Shinjuku, Vampire Hunter D, Witch Hunter Robin, Hellsing- are all worth a look.
Claymore- Is wonderful! Fullmetal Alchemist, Brotherhood- is fantastic. Those who hunt Elves (comedy)- is a guilty pleasure… Record of Lodoss Wars- Not bad, worth a look.
Steamboy- Good movie! Last Exile- I enjoyed it, not everyones cup of tea but I love aircraft.
Spirited Away, Howl’s Moving Castle, Nausicaa and the valley of the wind:), My Neighbor Totoro, Princess Mononoke.
Sword of the Stranger, Ninja Scroll- great movies. Moribito Guardian of the Spirit- a great series with a wonderfully rich and detailed fantasy world, and it is full of heart; I loved it!
Tenchi Muyo- a very old favorite. The Irresponsible Captian Taylor, Lum, Lupin the Third, Ramna 1/2.
Best anime movie I have seen recently is Summer Wars!
This is just a sampling of course… But it should keep a curious soul busy for awhile. Enjoy!