I love Gintama, only reason I didn't post it was because I'm not so sure a gag anime would fit what the OP was looking for. I have to thank you though because your post made me look something up and I saw they've started releasing new episodes - I had no idea.

Always been a fan of Cowboy Bebop and Neon Genesis Evangelion. If you had time for some cyber punk, classic Bubblegum Crisis. Berserk was a good anime as well if you want some fantasy.

If you really have some time, I would highly recommend Princess Mononoke as well as anything else done by Hayao Miyazaki.

Berserk
Fate/StayNight
Fate/Zero
Rainbow
Cowboy Bebop
Gintama

http://www.youtube.com/watch?v=8-fuhzhDNDc&feature=player_embedded
Has there been a western release for these? Apparently this is the third Berserk film.

Trigun

good story and action: cowboy bebop
overly bloody senseless violence but still good: hellsing ultimate

I haven't seen anyone mention any of these. Imho worth a try.

Azura Crying
Heroic Age
Zetsuen no Tempest (currently airing)
Magi (currently airing)
Claymore
Yondemasu-yo Azazel-san + OVA's (seriously messed up and funny at the same time)
Solty Rei
Seirei no Moribito
To Aru Kagaku no Railgun
To Aru Majutsu no Index
To Aru Majutsu no Index II
Katanagatari
Higurashi no Naku Koro ni Rei
Higurashi no Naku Koro ni Kai
Toradora
Yumekui Merry
Sora no Woto
Zettai karen Children
Tears to Tiara
Star Driver
Nurarihyon no Mago
Nurarihyon no Mago: Sennen Makyou
Towa no Quon
The Sacred Blacksmith
Welcome to the Space show
Summer Wars
Ladies versus Butlers (Funny and ecchi)
Seto no Hanayome
Shonen Onmyouji
Dog Days season 1 and 2
Mahoromatic season 1 and 2
Hayate no Gotoku season 1 and 2
Kekkaishi

There is a good site that is useful for if you loved one anime (e.g. Fullmetal Alchemist as you mentioned) and looking for other shows you might like in a similar vein. Each anime listed has a list of user-made recommendations underneath the description. The more people who recomend a show the higher its listed. Each also give their reasons as to why they feel if you liked 1 show (e.g. Fullmetal Alchemist) you might like the other and then you can pick and choose based on what sounds like the best match (some might be too vague a link, but I have found and enjoyed some anime I would not of otherwise of known about via this site).
http://www.anime-planet.com/anime/fullmetal-alchemist
http://www.anime-planet.com/anime/fullmetal-alchemist-brotherhood

(The site also has a system for keeping track of anime you've seen, are watching or Want to Watch etc. A bit like the Backloggery website does for games etc.)

I figured I'd come back and check for something to watch, then I go to the link sai gave, Darker Than Black was a recommendation, I thought it looked kind of cool, and it's awesome, it had me sad by the end of the 2nd episode... Anyways I noticed that nobody even mentioned this show, and I'm wondering why...

If you're going to watch Cowboy Bebop (you said you would, and you should), be sure to check Samurai Champloo as well. Not sure if anyone recommended it already, sorry.

Also, Trigun is amazing, as well, like Tiefood said.

Not sure if Monster has already been mentioned. Good story and animation, but it's very long (74 episodes).

My all-time favorite is probably Paranoia Agent. Me and my hubby devoured that one so fast.

If you'd feel like some comedy, I like School Rumble.

I probably should mention (since it's rather recent airing and if you don't mind subs) the new JoJo's Bizarre Adventure. While I love the OAV from mid 2000s, the 2012-2013 series was absolutely delightful. Though I recommend getting the uncensored version if you can, but that's just my opinion. :)

Last years were a letdown for me in anime genre. But anyway:

Steins; Gate - time-travel/sci-fi, great story, good characters and good animation
Gundam SEED (+Destiny) - for those into giant mechas and high tolerance to plot armors
Ghost in the shell - this one is a classic sci-fi, series are also great
Azumanga Daioh - best school comedy for me; no useless ecchi and toilet humor
Higurashi no Naku Koro ni - hard to describe without the word "disturbing" coming up in my mind; still, it is interesting
Great Teacher Onizuka - another great comedy with bits of teenage drama
Twelve Kingdoms - it may not provide a proper ending, but it's a fantasy series worth every minute of watching
Full Metal Panic - at times hilarious, at times dramatic; best Gonzo ever offered, imo
Kanon (v.2006) - tragic and touching, don't let the eroge origin fool you

Might be more that slipped my mind. Haven't been watching much of it lately.