seek said:
I was thinking of listing a few, but I really don't have a specific taste. Good anime is good anime, regardless of genre!
A few of my favourites include, Ranma, Love Hina, Ghibli movies, Bubblegum Crisis/Crash (Classic), 3x3 Eyes, Evangelion, GitS, Full Metal Panic, Tenchi Muyo and Chobits. As well as the old classic movies Akira, Project A-ko and all the rest.
So I guess from that list it's romantic comedys and the occasional sci-fi/mech type stuff.
Firstly I'll have to recommend the top 10 anime (not in order) I rate as the best I've seen (and I can cheat and copy/paste from ANN

)
Then I'll recommend some sci/fi, mecha, comedy, romance stuff.
Then I'll add a few more I rate highly and you might like.
Elfen Lied
I loved the story and the characters. I was amazed how they managed to fit so many different emotions in to the anime. There was a lot of bad stuff happening but an equal amount of good stuff as well. My first impression was that it was a comedy series as it was very funny although it did sober up a bit near the end.
Final Fantasy VII: Advent Children
I lost about 2 years of my life to Final Fantasy VII when it was released and I nearly wet myself with joy when I watched this. It might not have much appeal to anyone unfamiliar to the games but just seeing the team in full CGI beauty was a dream come true.
Gunbuster
I heard a lot about this before I saw it and I wasn't dissapointed.
It might be old but it's a great story, epic almost, especially the battles. I like Giant Robots and you don't get much bigger than the Gunbuster. The ending was moving as well and left me feeling elated yet sad at the same time.
Last Exile
Beautiful to look at. One of the best looking series I've seen but it isn't just flash and effects it has a great story and great characters as well. I'm a big Skies of Arcadia fan so the fact it had flying warships made me very happy as well.
Nadia: Secret of Blue Water
What a ride. I felt sad and empty when I ejected the last disc and realised my adventures with Nadia, Jean and Marie had finished. It might have got a bit ropey in the middle but I enjoy a bit of comic relief so it didn't bore me. Plenty of action in the rest of the series and a great story kept me glued to the screen.
ROD the TV
I enjoyed the OVA so I was looking forward to the TV series and it didn't let me down. More of the same, yet bigger and better. It looked nice and I loved the Paper Sisters, they made a great trio of heroines and they were fun to watch even when not doing anything exciting.
***RahXephon***
Simply the best Giant Robo style anime I've seen. I loved the fact it had an emotional side to it as well as the action. The animation was pretty and the characters were fun. Interesting story and Xephon just looked cool. One of the few anime I cried like a baby while watching, if you've seen it you know the part. Simply the best series I've seen so far. Everything about it just worked and I couldn't tear myself away from the screen until it had finished.
(Addition)
a lot of people compare NGE and RahXephon and claim one is better than the other but personaly I think they aim for different things and the feeling RahXephon gives out appeals to me more than NGE's does. RahXephon is a love story at it's heart and NGE is about a boy struggling to find his place in the world, and I'm a sucker for love.
Vampire Hunter D: Bloodlust
A beautiful film. The art style, architecture and general feel of the film were fantastic. The story was exciting yet also moving and D is simply one of the best hero characters I've seen in an anime. The whole thing comes together to make an amazing viewing experience.
Vision of Escaflowne
I love the whole schoolgirl taken to another world style anime and this is the best of those I've seen. It beats Magic Knight Rayearth by a small margin due to it's cleaner visuals and more dramatic storyline. A fantastic fantasy adventure with a host of interesting characters and the Escaflowne wins my 2nd best looking Giant Robot award. A fantastic series.
X TV
Much more than a supernatural fight anime. A deep and intresting storyline, multi-faceted characters and some touching love stories combine to make a great series. I also really like the CLAMP style of characters and this is the best of their work.
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Ok, now for some others.
Have you seen the remake of Bubblegum Crisis?
Bubblegum Crisis: Tokyo 2040 that's pretty good as well and not much different from the OVA, but different enough to be interesting.
Appleseed is a great looking film and a good sci-fi story. Well worth watching for the action and art.
If you like romantic stuff then you
HAVE to watch
Oh! My Goddess. It's just amazing and I'll probably nudge it up onto my top 10. There is also a newer TV series version but I haven't got round to watching it yet.
Photon: The Idiot Adventures is one you should watch if you like Tenchi. Very funny, a bit silly and features a boy with women all over him. (Although they dubbed a zoned out hippie voice on a young boy to make him seem legal

)
Excel Saga is hilarious. It parodies a different anime genre each episode as part of a sort of continuing plot line although most of the stuff is just random. One of the funniest comedy anime I have seen and you're sure to find an episode that makes you ROFL, literally (I did).
Giant Robo: The Animation is a fantastic mecha style anime. It mimics the 50's character designs but was made in the 90's. A very good story with some good characters. Sort of a cross between a super-hero cartoon and and mech show. Another series I might bump into my top 10 as I really enjoyed it.
Gravion and
Gravion Zwei are pretty funny mecha anime with plenty of fan service and over-the-top characters. Parodies the older style giant robot shows quite a bit.
Zone of the Enders is a pretty entertaining mecha anime with the addition of a squabbling family and a ditsy mech that thinks it's a little girl. Sounds a bit odd but it was very good.
Martian Successor Nadesico is a great sci/fi mech anime. I love the characters and I love the story. Avoid the film though as it is a bleak and harsh ruination of such a good series.
I can't recommend much romantic comedy stuff as I haven't got round to watching much myself, although I intend to remedy the situation soon.
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Finally some that aren't really in your watched genres and might sound a bit odd but are very good anime that I recommend anyway.
Angel Sanctuary might only be a short OVA but it is really the best manga advert ever cunningly disguised as an anime. I intend to pick up the manga series as soon as possible to see how the story develops.
It's basically an incestous love story that involves the corrupt forces of heaven, some badass angels, a few demons and a lad who contains the spirit of a heretical angel.
Chrono Crusade is set in the 30's I think. About a girl who fights demons but is seems to ***** it up a lot and her demon companion. It starts silly but gets more serious towards the end. I really enjoyed it.
Magic Knight Rayearth 1 + 2. The first series is slightly better than the second but I just love schoolgirls in alternate world anime. Also features mech of a sort and some romance but it's very girly so might not be your cup of tea.
Master of Mosquiton is a pretty daft vampire story although it does have a semi-coherent plot and looks nice. Very funny though.
Rune Soldier is a fantasy comedy. You have to love a magician who prefers to hit things with a stick rather than use magic. a lot of fun and I liked the characters.
Witch Hunter Robin is very good. About a bunch of church run witch hunters that chase down rogue psychics. A very interesting story and good animation. It gets dark in some places but has plenty of action as well.
Wolf's Rain is about a group of wolves who can look human searching for paradise. Sounds a bit odd but is very good, the characters develop well, the post-apocalyptic setting is good and it carries on at a good pace.