CHAMPLOO, It's Samurai Champloo! Argh!

Tengen Toppa Gurren-Lagann!

 If you can sit here and tell me that G Gundam is the worse Gundam series ever, you must not have seen Seed/Destiny. Honestly, what's wrong with G gundam? What didn't you like about it?

Three Words:

Chibi Vampire Karen

Oh yeah, also:

Cyber City Oado

and

Love Hina

There are a lot of good, underground anime's listed in this post.

For a n00b, I suggest starting with:

Ninja Scroll movie

Hellsing(which will prepare you for)

Elfen Lied(time to calm down with)

Vampire Hunter D: Bloodlust(which will give you significant enough background to watch)

Spirited Away(and climax in your knowledge with)

FLCL 

At this point, you should be able to decide for yourself, with some of the more underground ones.

When you're ready, you should move on to more advanced Anime's like Monster. 

Note: I highly recommend seeing (sp?) The Melancholy of Hurhai Suzimiya as soon as you've reviewed the basics. It's an uplifting anime that is a must see.

Gundam Seed has quite a bit of angst but it has some redeeming moments and some decent character development. It turns out to be thoroughly mediocre. G Gundam is a like a sick joke. It has the worst premise of any Gundam series and ranks up there among the worst premise of any serious mecha series. I'd rate it just above Fafner in the Azure (which I can only assume was written by asexual monkeys with typewritters). If you are watching G Gundam, you're not watching it for character development or deep story. Domon is a walking cliche and the plot is lame. The entire show came down to who fights who next... and I'm not a fan of villain of the week unless it's Ranma 1/2.

Asking me what I don't like about G Gundam is a fair question and I hope that about covers it.

Check out Yu Yu Hakusho, Its my personal favorite.

Above posters gave some good choices like,claymore and hirugahsi. Since those are gritty anime I suggest two more. WITCHBLADE SPEED GRAPHER I wrote them in big words because that how much I adore the two series.

I've always liked Inuyasha. The Character interactions are all very funny, the characters develop, and its easy to understand for the most part.

No love for Hajime no Ippo?  BLASPHEMY!  You liked the Rocky movies then I would highly recommend watching Hajime no Ippo, it's one of my favorites next to the Melancholy of Suzumiya Haruhi.

Animes you might enjoy (some I don't really enjoy much mind ya'll):

Inuyasha (meh, fair warning:  the ending is god awful)
History's Strongest Disciple Ken'ichi (it's ok, the fighting scenes are cool but not the best)
Hajime no Ippo (boxing anime.  I completely love this anime, give it a shot to see if you like it)
Hunter X Hunter (I haven't actually seen this one but it reminds me of Naruto)
Hellsing and Hellsing Ultimate (Ultimate is far better in action and story in my opinion, but the first was pretty although there were no Nazi vampires)
Trigun (it's a classic, it just demands your attention)
Cowboy Bebop (really liked the characters, also pretty much a classic)
Samurai Champloo  (if you liked Cowboy Bebop definately go on to this one.  The sword fighting is great, and I love the characters, especially Mugen)
Berserk (one of my favorites, but the ending will leave you wanting more since it ends on the part where things start to get really good.  Pretty much no humor, its a pretty dark anime once it approaches the ending)
Speed Grapher (weird  anime, but really cool.  I wish I could blow stuff up with a camera...)
One Piece (Naruto except with pirates pretty much)
G Gundam (apparently some people here don't like it but I did.  It's not a traditional Gundam anime, but that's fine by me.  It's really silly to watch mechs kung fu fight but also cool at the same time.  Burning Fingers!  Lmao)
Tenchi series (probably might not be your cup of tea, but I liked them)
Buso Renkin (haven't watched this myself yet but my friend enjoyed.  It seems to take some elements of alchemy from Fullmetal Alchemist and the main character has a sword...  No harm in giving it a shot, eh?)
Tenjou Tenge (fighting is pretty cool in this one, but I thought the story wasn't all that good)
GetBackers (I watched one episode and didn't like it too much.  Some people like it, others like me don't.  Maybe you'll like it)

I can't think of anymore right now, but if you liked my suggestions are try to think of some more. 

 Devilman?.... is it a Manga anime? might give it a try