Title says it all , I wouldn't be providing names of Animes such as Bleach or Inuyasha nor any long running Animes , however. I'll also try to provide a representative from each Genre ( Action , Comedy , Suspense / Thriller / Gore , Romance etc. etc. )

Action / Political :

1. Full Metal Alchemist

Funny , quirky , yet serious and intense at the same time. Full Metal Alchemist has finely delivered political affairs , alchemy ( magic ) , comedy and the suspense of the atmosphere without overlapping nor smearing either of it's content and has finely delivered a storyline filled with plot twists , thus , the audience would never befailed to be surprised.

Romance / Slice of Life :

2. Spice and Wolf

Who says that romance Animes need to utilise the words "love" in a touching scene? The characters often use the words "like" as a passing remark but not a single utter of the word "love" in an obvious scene that suggests romance. However , the soft , sweet romance in this Anime definitely would not disappoint , especially in Season II where we see the characters go through simple emotional struggles yet is able to play a chord in your heart at the same time.

War / Political / Action :

3. Code Geass : Hangyaku no Lelouch

Code Geass , some points of it are obviously Death Note rip-offs such as the restrictions of the Geass but that doesn't stop it from being an Anime of epic proportions. The characters aren't perfect and once again , we'r thrown into two different sort of justice involved in the struggle between two forms of power. The first Season is Zero spreading his influence and power in Japan and the second season gets a bit more political and concludes Lelouch's conquest. Interestingly , the side characters play a certain extent of role in the Anime as well. This is also a nice twist from CLAMP's usual works and is a must watch.

Comedy :

4. Seitokai no Ichizon

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I found an Animated pic so I might as well use it XD

Well , this Anime mainly lives off it's Comedy content. The story only starts to kick in , in like the 3/4 part of the Anime. It's recommended that you watch plenty of well-known Animes before watching this otherwise you won't get half of the puns. Baka to Test is a really good Comedy as well so do take a look.

Music :

5. Macross Frontier

When the words "Music Anime" is involved , I'm pretty sure the first impression that comes by is K-ON! so I might as well select something else :P

Either way , the Mecha design definitely won't appeal to Gundam fans since the Mecha is like...stuck in their airplane forms most of the time but the music , especially Don/t be Late by May/n makes the battle sequences 2x more epic than usual.

Action :

6. Fate / Stay Night

Fate / Stay Night...well , I really have a dilemina on what to put for the Action sector. Either way , Fate / Stay Night poses a delicate balance between storyline and action sequences in the limited amount of episodes it have which is obviously not enough to tell the tale of the original storyline , like most other Animes out there. The action sequences isn't all that impressive , for that you might as well watch Gundam or long running Animes. However , the general storyline is great and the cast of characters are likeable.

Game Based Anime :

7. Tales of the Abyss

Amongst all the Game-Based Animes , Tales of the Abyss have to be the most appealling , even amongst it's Tales Anime bretherens. Sorry Persona fans! XD

Mystery / Suspense :

8. Monster

One of the most suspending and interesting Mystery Animes of it's age and time. As of late , there are many mysterious and horrendous crimes in place and a doctor found out that the person behind it was a boy he had seen a long time ago in an operation room , where he was shot directly in the head. So who exactly is this boy?

Gore :

9. Higurashi no Naku Koro ni

You'd probably think I'll put Elfen Lied but doing that is way too boring for the list. Higurashi no Naku Koro ni started off innocent like any other Animes out there in existence. However , as the plot progresses , the audience would have to put themselves through disgusting murder to suicide scenes and even seeing the culprit indulging themselves in their acts at times. It's like seeing the School Days ending sequence again and again and again through out the Anime...oh boy.

Harem :

10. Princess Lover!

For once , I think I managed to enjoy a Harem Anime. Well , if your wondering , I'm do not consider Clannad , AIR and Kanon as Harems since the ending and the cahracter's decisions clearly shows nothing Harem-like. Either way , for once , the main character isn't a useless bum in this Harem Anime , he can even use a katana...The conclusion of the story is fairly interesting as well I dare say.

Well , for Part II , I'll do other Genres and repeat certain Genres if I have to so don't worry if your favourite Anime isn't in the list :P