Oh dear god how much anime I watch, I won't be able to list it all. I do prefer the actiony and quicker paced animes. Not really in a particular order.
The Good Stuff:
Ergo Proxy - post apocalyptic sci fi mystery with a scary lady
Seirei No Moribito - Follows the spear fighter Balsa and this kid she has to keep from being killed by his Emperor dad.
Ghost in the Shell (all of it) - Motoko is the future's Sherlock Holmes
Canaan - Terrorists use scary biological weapon on civilians, the story follows two girls, one a cameraman, the other an assassin.
The Melancholy of Haruhi Suzumiya - You must watch this show.
Black Lagoon - Ransoming giant warships with rocket launchers ftw
Darker than Black - Post apoc supernatural mystery anime. Good show.
Last Exile - Steampunk, airships, vanships vanships vanships
Witch Hunter Robin - Setting people on fire with your MIND
Hellsing Ultimate - Over the top vampire action
Vampire Hunter D - Another holycrap awesome vampire anime.
Ga-Rei - Demon fighters or whatnot. Really damn good story, scary scary people. HELLO KAGURA~
Black Rock Shooter - Tis about friendship and fighting in other dimensions. They need to make this an actual series.
Gurren Lagann - How giant robot animes should be. One of the few animes that have an actual male character that acts like a man.
Samurai Shamploo - This girl hires some samurai to help her find a dude that smells like sunflowers.
Ah My Goddess (2005) - Horribly goody goody but still I can't stop myself from watching it. ._.
Full Metal Panic - Giant robot action, a bit of violent comedy, and a mystery~ Epic soundtrack.
Read or Die OVA - It's like a British secret spy action flick. The chick fights with paper. WITH PAPER.
Le Chevalier de Eon - Guy's sister gets killed and he goes to find out why. Sister possesses brother to pwn bad guys. She's scary.
Soul Eater - Pretty stylish anime. School run by a Shinigami, some kids can turn into weapons and fight bad guys.
Battle Angel Alita - Cyberpunk cyborgs ftw. Ended early and they never revived it.
Crest of the Stars - Pretty old anime. Space battle action. I still like it.
Banner of the Stars - Sequel to Crest of the Stars.
Slayers - It's fairly old and has lots of different versions. Mostly follows a midget raging sorceress and her shenanigans.
The Funny Good Stuff (and probably nsfw):
Panty and Stocking with Garterbelt - Angels that got kicked out of heaven, have to kill ghosts to get back. The animators like to troll you.
Deadleaves - It's like an animated comic book. Just as silly as Panty & Stocking.
Cromartie High School - Stuck in a whacked out school for delinquents. Ogodwhat.
Abenobashi - They get stuck in another dimension, parodies happen.
Hare & Guu - Hare meets Guu. Guu destroys his reality without any mercy.
Excel Saga - This one may blow your mind. But this is nothing compared to it's successor...
Puni Puni Poemi - What they couldn't get away with in Excel Saga. You have been warned.
Fooly Cooly - This show. This show parodies things and goes beyond the imagination of wat.
Lucky Star - Bunch of weirdo kids in school doing weirdo things.
Anime Movies:
Anything made by Studio Ghibli (Howl's Moving Castle, etc.)
Appleseed - The movies kinda lacked a bit of story but they were still pretty awesome.
Steamboy - It's freaking awesome. I still don't know who the bad guy is.
Slayers - There are quite a few Slayers movies, I watch them for the lols.
I will list moar as I think of them. My manga list is far far longer.