Why has nobody mentioned Trigun yet,it’s a very good anime and gives you good laughts see it ASAP.
And follow the sugestions of all of above.
Dual: romantic comedy sort.
Has a Tenchi feel to it(all the girls flaunting over one guy). A guy is sent to another dimension that has giant robots fighting a war. He gets to pilot one of the robots once they discover he’s really good. More things are going on, but I’m really bad at reviews/summaries whatever. ^^;
Tenchi Muyo Ova/series whatever: romantic comedy-
Check out the Ova or one of the movies, they are all pretty good.
Slayers- Fantasy genre. Tone can range from light-hearted comedy, to very dark. It follows the adventures of genius sorceress Lina Inverse as she saves the world time after time, somewhat reluctantly, with the help from some pals. One of the original anti-heroes.
RahXephon- Science-Fiction. Similar to Evangelion (scarily so), but less mind-blowing, and dealing with music instead of religion. Tokyo is separated from the rest of the world by alien invaders. Time runs slower there, and the inhabitants believe that the rest of the world was destroyed. Ayato is pulled out from Tokyo and enlisted by the military to pilot RahXephon against the invaders.
Vampire Princess Miyu- Horror. Miyu’s duty as Guardian is to send stray Shinma (demons) back to the Dark. She must also fight against those who wish her dead with the help of her companions Larva and Shiina. Frozen in the body of a fourteen year old, Miyu befriends a girl at the school she is currently attending, which arguably begins to cloud her judgement.
Trigun- Western/Sci-Fi/Comedy/Angst. And somehow all those genres don’t conflict with each other… Vash the Stampede wanders a desert world with a $$60,000,000,000 bounty on his head. Meryl Strife and Millie Thompson are insurance girls assigned to find and follow him, in hopes to keep his property damage down. But goofy Vash has a dark past that is rapidly catching up with him.
Not sure if I did justice to the summaries for those series’… Just a few suggestions, anyhow. 
I don’t know about the show, but I used to read the Ranma 1/2 manga’s all the time, and they’re actually really funny. It’s about this guy, Ranma, that was training in the mountains with his father (it was complicated stuff…imagine sort of a rice field with bamboo halves sticking up out of little clearings in the water.) Myth went that each little pond had a curse, and if you fell into the pond, you would be cursed. Well, Ranma fell into the pond of drowned girl, and his father fell into the pond of drowned panda. So now, whenever either Ranma or his father, Genma, are drenched in cold water they become a girl and a panda, respectivly.
Then Genma takes himself and Ranma to live with an old friend at his Dojo. The old friend has 3 lovely daughters, the only one of which I remember is Akana, the budding love interest. The sexual tension between Ranma and Akana spirals out of control when his secret is revealed, and the hilarity ensues.
No mention of Saber Merriontette J, my first anime, it got me hooked. I’ll keep this short by saying it starts out funny, then progresses into the more serious, pans out to be one of the best plots ever. I guess it won’t spoil anything to give the basics, Terra II is an all-male planet, everyone is clones with genetic manipulation (there was an accident with a space colonist ship, only 6 guys survived, no women, so they got into the cloning business. Main character has 3 female robots in love with him, rated Pg only for violence, no nudity and only a couple mildly suggestive scenes mostly in the 5th episode.
Soul Hunter: Based on an old chinease novel (really old novel) but it’s a fairly recent anime (just a few years old). Rather than have me describe it go see it for yourself.
Slayers Next: WOW, it was increadible, like the first series (Slayers) it switches between serious and comedy, naturally your required to watch Slayers before Slayers Next and Slayers is good to, but Slayers Next was the best.
Matanaki Loki Ragnarok: To the best of my knowlage this still can’t be found in America, look for fan translations. This series is Norse Mythology taken from Loki’s perspective, only he’s been banished, had most of his powers sealed, and is trapped as a small child living in Japan, then decided to open a detective agency. Sound wierd, don’t worry most good anime is bizzare (look at how many people listed Excel Saga, it doesn’t get any wierder then Excel Saga… Except maybe for FLCL). Anyway the guys who made it really know Norse Myth, everything they changed was changed for a reason, and the Midgar Serpent is the most awesome character ever (yes one of the main characters is a serpent so large it surrounds the planet), also wait 'til you meet Fenris. Awesome awesome series, there’s so much more I’d like to say but I don’t want to spoil it. Don’t worry, the girl doesn’t get on your nerves so much after awhile.
Well there you have it, there are many great anime but those are my top 4. past that is Kenshin, Trigun, Ushio and Tora, and countless more. I founded an anime club and am in the process of gathering enough anime to open an anime rental store. I’ve only met a couple people who have seen more anime than me.
Oh yeah, I waited for years for Star Ocean EX to come out, I gotta get ahold of it still, and not another really bad Korean sub job (what was my mother thinking?) If that meets my expectations that’ll be another one to look out for. Course I’m already mad at thier depictions of Ashton (The dragon were fearsome in the game, not overly cute!) and Rena (she’s portrayed as being to young, in the game she seemed adult) However these are only going by the pictures I’ve seen, it would be so awesome if they got the voice actors who did the translation of the game… However unlikely that may be. Anyway you may want to keep an eye out for this one as well, and if you havn’t already played the game hurry up and buy Star Ocean: The Second Story. It was produced by Enix.
SOEX was pretty disappointing IMO. I’m not so much mad that it wasn’t true to the game, but that there’s a reason why the game had things the way it did and the changes they made (mainly to the plotline after the Lacour Tournament) were not good changes. It really started to bore me after around episode 16 or so.
X was good, albeit a little corny. The last couple episodes make the series worth it.
Cowboy Beebop is excellent. I’m sure you’ve heard a lot about it.
Excel Saga is a weird and parodies A LOT of stuff. I liked it.
Kare Kano aka His and Her Circumstances is awesome. And this is coming from me of all people :P. Its about 2 top notch students who fall in love and their friends. Who would’ve ever though Sin would endorse something like this? Its that unusual. Its a must see.
And Wilf: you forgot to say “Its not porn, its art”.
blink blink Umm… yeah. FLCL IS pretty fucking weird. I love it- but I have zero clue about what is going on… and I know I’m not alone.
Cowboy Bebop on the other hand- I fucking love it. Yeah, these are the only two I got to check out so far… but I’m pretty poor. =p
Now, that Matanaki Loki Ragnarok one… hmm… I think I’m going to have to DOWNLOAD that one, 'cause if it isn’t released in English… well- I can’t understand Japanese. =p
If you like any of the stuff by Leiji Matsumoto that Igatona mentioned, then I’d check out Arcadia of My Youth. It’s a prequel to the Space Pirate Captain Harlock series in which Captain Harlock, with the help of a group of friends, has to battle an alien race who took over earth. My description might not make it seem like much, but it’s a really great movie.
Ranma 1/2
Angelic Layer
Kino’s Journey
Chobits
Neon Genisis Evangelion
Blue Seed
Princess Nine
Azumanga Douhi
Sorcerer Hunters
Final Fantasty: Unlimited
Eden’s Bowy
Gravion
Nuku Nuku
Neo Ranga
I compleatly forgot one of the best anime series i have seen up to date.
The Twelve Kingdoms:Youko Nakayima is a high school student,president of her class and tries to be liked by all.However this all changes when she is taken to the world of the Twelve Kingdoms,she starts distrusting everyone since anybody she trys to ask for help betrays her.What she does not know is that she was chosen by the heavens for a huge task
What i just told you is just a small part of what the series is about and by small not even 1/3 of the hole story,It is very,VERY good series see it ASAP.
Sin: I was too distracted by your hair. 8P
OK, getting serious again:
Loki, do you get Tech Tv on your cable line-up? They have a show called Anime Unleashed! that features various dubbed Anime Ovas. I think you would like most of the ones they air. If you do, I can describe some of them.
I don’t believe that I do, and I don’t really watch television anyway, commercials anger me. I either download or rent TV shows. Also, I don’t really want them edited.
I recomend that you get Comcast Digital Cable. It has a thing called On Demand that has Tech TV, and an entire network devoted to anime!!! Or just get Kazza.
Oooooh, yay! Anime! LOL.
Zone of the Enders: (Watch the movie Idolo <i>before</i> the series, Dolores.i, if you look into it)
Earth and Mars are always at political odds with one another, but the scientists of Mars have discovered and honed an ancient technology dubbed Orbital Frames. These mechs emcompass incredible amounts of power, but the planetary war isn’t hot enough for them to be properly employed… Idolo is very series, where as Dolores.i can be very series, but is also extremely funny.
Flame of Recca:
Recca’s always wanted to be a ninja, and when he finds out he has mystical flame powers, his best friends becomes endangered, and someone seems out to kill him, he finally gets his chance to live his dream… however silly and over confident he may be.
Trigun:
Vash the Stampede is a mysterious man with a $$60,000,000,000 bounty on his head. But who is he? Ace gunman or blithering idiot?
Witch Hunter Robin:
The STNJ is charged with protecting the peace. Their targets are witches. Fighting the Craft users and trying to identify with one another are the least of their worries once other agencies target the STNJ…
.hack//SIGN:
In an online game, The World is a vast 3D environment where everything starts to go wrong. A user gets trapped in the system, monsters who can’t be killed start to appear, and not even the system admins know what’s going on. The quest to figure out what’s happening isn’t easy…
Haunted Junction: (Comedy, sorry, but I love this one. It’s only like 12eps…)
A school that’s the most spiritually charged point on the planet has a lot of weird things happen. With a violent Shinto Pristess, a spiritually hyper-sensative monk, and the son of a Christian priest who wants nothing to do with the supernatural as the student council, nothing normal ever happens.
Cowboy Bebop:
Spike and Jet are bounty hunters who just like to get the job done, but when Faye, Radical Edward, and Ein the dog get brought on as crew one by one, life gets more complicated… and they had enough money problems before hand.
Outlaw Star:
Gene Starwind and Jim Hawkins as bounty hunters on Earth until they run into an imfamous pirate and a girl in a suitcase. Getting their own ship with the Kay Pirates organization out to kill them makes life extremely difficult, but someone they manage… disregarding an incredible amount of debt.
Full Metal Alchemist and Full Metal Panic I hear are good, but I haven’t seen them.
Some of them are really silly at times… but they’ve all got their series points. A movie I like is Jin Roh: The Wolf Briggade… I also like the Ah! My Goddess movie. ^_-;
Series that I would suggest:
Neon Genesis Evangelion: It starts out like just any other Giant Robot Anime, and it’s really crappy at first. My friend had to FORCE me to watch almost 1/3 of the series before it started getting good. It really gets a lot more in depth than any normal Giant Robot Anime, and presents some cool mysteries, though they’re not very well solved mostly. The main focus of the series I think, is the social interactions, and the psychology and philosophies of social interaction that are presented; every character in the series has some sort of serious psychological problem. And, thusly, the most interesting aspect of the series is watching these people interact, regardless of their problems. It’s interesting.
Cowboy Bebop: Well, I see you already like Cowboy Bebop… 
It’s really more like American TV (Less story, not booklike, no continuity, etc.), and that’s why I like it. Plus the music is just awesome.
I don’t know if I can reccomend any other anime. The truth is, I don’t really like anime Those are the only two I like. I’ve seen a lot though, cos I’m the only anime hater in my clique/posse/whatever, so if you want to know an anime or two I think you SHOULDN’T watch, and why, then you could ask me.
Samurai Champloo is great. kinda like Cowboy Bebob in feudal Japan.
It’s amazing how many people have heard of Scrapped Princess, despite it’s unavailability in the US. Yeah, that’s my primary choice, right now.
others are:
Tenchi Muyo-this one does the “guy with a bunch of girls” theme the best. There’s tons more going on too.
Sailormoon-Screw that cartoon network crap. Get the uncut stuff. Go find sailor stars. Search for VKLL’s fansubs, or go to www.aoshianime.net
Love hina-the Aformentioned “Guy with a bunch of girls” theme, but there’s not a whole lot more going on. Its’ just a fun series, if not a bit redundant.
Chobits-A cute sweet romantic comedy romp. Chi is just adorable with her innocent nature, and the story is metaphorical for how obsessed people are with convient gadgets.
Yumeria-Yet again, the “guy with a bunch of girls” theme. This one is far more… racy. It’s pretty mindless too. There’s a Power Rangers-type subplot, that seems sorta tacked on. It may not be, I dunno, i’m only on episode 5. But after watching something as heavy handed as Scrapped Princess, its’ a very welcome change of pace
It’s important that you get your anime subtitled, as the english scrips and acting suck pretty hard.
Now, where to find it.
www.section9anime.net has the whole chobits series for d/l. if you got cable, you can get the whole series in a half hour. It’s got eps 3-10 of Yumeria, and their working on getting all of Scrapped up. I’d wait till they get em all (8-11, and 20-24 are down) cos you’ll be stuck at episode 7, like I was and be VERY pissed off.
There’s torrents too. Animesuki, I think is one, and downloadanime.com get a torrent downloader, www.bittornado.com is a good one.
You can also buy these series, obviously. Go to www.animeARIGATO.com, or www.discountanimedvd.com. They got whole series imported for like 30 bucks. (all 24 eps of scrapped princess, and chobits, for instance are 30 bucks) www.rightstuf.com is another good choice. They got a ton of crap on clearance dirt cheap right now, and they got weekly specials, and daily specials and all that.
Hope that helps you somewhat. I’m just getting back into anime myself, so I got some catching up to do. I’ve been obsessing over it in the last week. Trust me a week ago I wouldnt have known about any of this, cept sailor moon and tenchi.
I haven’t seen that many but of the ones I’ve seen .hack//sign and Inuyasha are my favorites. I’ve seen all the ones cartoon network has and a few episodes of Last Exile.