General

OK , Serious anime fan here, Bleach is arguably the best anime, that will be the baseline for " good" , lots of good anime has already been mentioned

The irresponsible Captain Taylor - Very funny, Space theme, Retro animation( 80's) not a down side though and the best Dubbed voice acting since Dragon ball Z
Beelzabub - Pure ridiculous laugh of loud fun, one of the funniest about, ratings reflect that.
Fairy Tale- Good style, fun ,flashy and no fillers , saga's last around 10-15 episodes then its straight on to the next, lots of fighting, mythical rather than science, woulds watching for a maple story style

Ok there is 3 Very good anime, on par with the big ones

as others have said
Darker than black- Dark and violent,
Full metal alchemist- Good and fun, nice power levels , first episode sets the tone nicely/ not very nicely at all
Psycho pass - Dysitopian future , good sharp style , nice themes and so horrifying images , well worth a watch

And a few more
Gurren Lagann - Arguably one of the best "mech" anime's , very bright and fun , real sense of justice and a reason to fight, loads of varying mech's
Black Rock Shooter- The most amazing messed up anime created , very " borderline" honestly words cannot describe
Evangelion movies - Might of seen them, but the movie's are very good

Wouldn't really call any of these Echi and not too sure what echi is, Normally got for fighting based Anime's

If I had to recommend one to watch, to everyone

BEELZABUB!

Tough question to answer when everyone has seen so many ,
Happy viewing

try bakemonogatari, few ecchi and action scenes there and here, but mostly character interaction and epic dialouge

steins gate

The first thing I thought was of The Qwaser of Stigmata/Seikon no Qwaser. *cackling*
Oh great I will never get that anime out of my head anymore.

Watch Clannad then Clannad Afterstory

@RisingRain: There are aspects of ecchi, such as their IS post-transformation outfits, Some fanservice scenes and other whatnots.
Also, Romance and Harem come hand in hand, You can't have a harem without a romance.. can you ?

[quote=alltwo147]Full Metal Alchemist

The original or Brotherhood is fine, but watching both is great.[/quote]

Brotherhood is the original

They decided to make their own animated version which is FMA, then finished the original work which was called FMA: brotherhood

LISTEN TO ME
Full Metal Alchemist Brotherhood
Code Geass
Asura Cryin
Zetsuen no Tempest

have fun crappin urself in the loss of sanity

[quote=MybulIets]Romance/ Ecchi* / Si-Fi /Action.

Only thing that comes to my mind is Infinite Stratos. Not sci-fi, but mecha.[/quote]
Lol, IS is harem that just happens to use mecha.
Code Geass might be something to try if you're into Mecha/Sci-Fi/Action. It's a glorious trainwreck, just like GC (though imo better).

Romance/ Ecchi* / Si-Fi /Action.

Only thing that comes to my mind is Infinite Stratos. Not sci-fi, but mecha.

Full Metal Alchemist

The original or Brotherhood is fine, but watching both is great.

anohana is the only anime that made me cry every single episode

Sakurasou no Pet no Kanojo is something I'd highly recommend. One of my favorite animes ^^

Give Kakumeki Valvrave a go

Season 1 is finished and Season 2 is still currently airing

I have more I can recommend, but these are the ones that kinda follow the genres you wanted:

Attack on Titan
Darker than Black
Eureka 7
Pandora Hearts
Shakugan no Shana
Suisei no Gargantia
Sacred Seven

watch Fairy Tail

i read all the mangas u listed already

I've found the first episode kind of gory, but you said you life sci-fi right? Try Psycho Path? I think thats the name, but try looking that up, has good art xD
Edit: Nevermind, I think its called Psycho Pass