I highly recommend Trigun. It's solid gold from beginning to end.
Scrapped Princess is brilliant. I can't recommend it enough.
You should also see FLCL. It's quite bizarre, so you might even want to watch it twice to figure out what's going on.
The Full Metal Alchemist anime is very good. Someone suggested holding off for the new Full Metal Alchemist series, but since they follow different storylines you could conceivably watch both. The movie "Conquerer of Shamballa" or something is not quite so good though.
If you liked Cowboy Bebop and its unusual style, then you'll most likely love Samurai Champloo. It has the off-beatness of Bebop, but is about ronins in feudal Japan.
If you want to watch a long-running series, try Naruto, but watch only until episode 135. Episodes 136-220 are pretty much pointless fillers that add nothing to the story. The real story continues with the next series, Naruto Shippuden.
Haibane Renmei is worth watching, but be warned that it is neither action nor comedy. I'm not really sure how to describe it, but it's an interesting take on afterlife.
I enjoyed Slayers very much. It's a well-made swords-and-sorcery with a very eventful storyline and an interesting sense of humour. In case you're wondering where to start, the first season is simply named "Slayers", followed by "Slayers Next", and then "Slayers Try". After that comes "Slayers Revolution" and "Slayers evolutionR".
Trinity Blood is a nicely-done series similar (but in many ways very very different) to Hellsing. It has a somewhat unusual premise of attempts to forge peace between vampires and the cyborg-catholics :P

Try FLCL it's only 6 episodes long, but it will totally rape your mind.

all of you guys rock, this thread is getting favorited until i have seen every single one of these

This alone makes me want to see it, though I never bothered with Hellsing.
Last Exile and Ergo Proxy sounds like good suggestions as well (I already watch or have watched many of the others being mentioned).

Fitzy, Read or Die the TV. Get it, its short, sweet and amazing.

I think it's one of those things you either love or hate. If you take it at face value, it's an average mecha anime with a lot of plot holes and confusion, but if you pay close attention to the subplots, themes and hints, you find those plot holes filled quickly. Since it's only one season long, it's easy to rewatch it a few times and figure out most of the details. Alternatively, the Wikipedia articles on Evangelion are /extremely/ thorough in explaining everything, but also very spoily, even if you've already seen the show.
Anyway, I feel the same way about Akira, and I think that's because I never went back to figure it all out. The end of it baffled me, and so did my friends' explanations.

Actually, I was constantly irritated by main character, I loved the plot otherwise

On that note, Millennium Actress. Not as mindfucky as Paranoia Agent, but probably Satoshi Kon's best movie--about as tearjerking as an animated movie has any right to be.
Most of what would have been my other recommendations are already covered here, but as you've already said you liked Cowboy Bebop, I'll have to go with the crowd and give Samurai Champloo another push.

I'd definitely have to give an extra push on Outlaw Star (Don't forget Episode 24!)
and Samurai Champloo (gotta love the initial warning on the "historic theme")
as well as Elfen Lied (awesome if you like the idea of boobs blood psychic gothic anime)
Neon Genesis Evangelion is a good mind fuck but along with that Gantz is a decent one as well... if you like comedys I'd have to suggest chcking out any of the Full Metal Panic! series, either of the Please! series, a couple of the Tenchi Muyo (so sue me.... the cat fights are fun to watch), Desert Punk, Mezzo, Maburaho, Rune Soldier (also known as Lewie the Rune Soldier), Girls Bravo, Ikki Tousen, Martian Successor Nadesico......
if you like a semi serious tone to it (at minimum) and like steam punk(ish) Texhnolyze was interesting and of course another push for Last Exile....
Other series I can suggest: Zaion, Daphne In the Brilliant Blue, Love Hina, The Devil Lady, Escaflowne, Crying Freeman, Chobits, The Irresponsible Captain Tylor, Black Heaven, Yumeria, Those Who Hunt Elves, Peacemaker, Girls BRAVO!, Witch Hunter Robin....
I still have to finish watching Noir, Madlax and Misaki Chronicles as well as another viewing of my just completed Witch Hunter Robin and L/R collection ^^...
oh and those who have mild social ineptitudes might find Welcome to the NHK quite entertaining (the main character has inadequacies up the ying yang) and Tenjho Tenge and Stellvia weren't that bad either

You should try watching that one where the girl gets raped by tentacles, it's pretty sweet.

There's a reason that Neon Genesis Evangelion is depressing; the entire thing is basically the result of the depression suffered by Hideaki Anno.
Also, if you're going to watch Graveyard of the Fireflies, get yourself My Neighbour Totoro to watch immediately after to get that true 1988 cinematic experience =)
As for recommendations (movies):
The Girl Who Lept Through Time (toki wo kakeru shojo)
Summer Wars
Appleseed (2004 remake)
Appleseed Ex-Machina
Vexille
Whispers of the Heart (mimi wo sumaseba)
A Chain of Short Stories About Their Distance (byousoku 5 senchimeetoru)
The Voices of a Distant Star (Hoshi no Koe)
Series (light-hearted parodies of a bunch of other stuff):
Genshiken 1 and 2
Keroro Gunsou (Sgt. Frog)
Unfortunately, I have no idea of what the availability for any of these is like outside of Japan.

His fans didn't exactly help either, when they sent him death threats and complaints when they didn't like the original series ending.
The Girl Who Lept Through Time was also a good movie. That one's definitely around outside Japan. Never heard of the others though, so I'm not sure.
While we're at it, all the Studio Ghibli movies (inc. Grave of the Fireflies & My Neighbour Totoro) are fantastic. Some others to grab are Spirited Away and Howl's Moving Castle.

This is a long shot but has anyone seen an anime about a wizard type guy who has a girl and an apprentice following him around. I only saw one episode but the apprentice was supposed to light a rock on fire but he accidentally lit charcoal on fire. There was also a cave-in i think.

Hentia isn't anime right?

Sounds vaguely like Howl's Moving Castle, but that was a one-off movie.