That's way too many qualifications. You can't ask people to suggest things and then list 13 qualifications. Why should we help you if you're not even going to be open to the genre? That said, watch Cowboy Bebop (as already suggested). And if you're willing to ignore the fact that it's not sci-fi, Case Closed/Detective Conan.

I also have to recommend Lupin the 3rd.

Shit I cannot believe I forgot Lupin and Conan. Lupin the Third in all of its forms is wonderful, you can't go wrong. Very silly, though.

Seriously though.

Cowboy Bebop and FLCL.

how about "Now and Then, Here and There"? it has war in it but it's more focused on the characters...

Grave of the Fireflies is good too, but that's a movie.

Oh, I bet you'd love Spirited Away. Spirited Away is excellent. My favorite Miyazaki film.

I like fighting, I just don't want it to be the only focus of the show (plot and everything else are just flimsy structures to allow for endless fighting sequences).

I tend to agree with about 95% of your thoughts/opinions about games, so I'll most likely give Cowboy Bebop a shot.

Your requirements are very much contradictions, if you like Sci Fi/Fantasy but you remove all those options then theres about nothing left.

That would be like me saying 'whats me a good Sci-Fi show but no technobable, time travel, fighting/wars etc'

Thanks everyone. And Montanta, I wasn't giving a bunch of qualifications and saying "OKAY GIVE ME THIS SHOW", I just wanted to give a loose feel for my general preferences so those of you more intimately acquainted with anime could steer me in the right direction. I'm actually very open to pretty much anything and tend to force myself to read/watch/play things I'm not familiar and comfortable with, just to broaden my tastes. Just thought it might help this spark of interest catch into a flame if I fed it a more readily burnable fuel.

I have watched all Studio Ghibli films and love them, just never any serialized anime.

@Squilliam I only mentioned a preference for Sci-fi/Fantasy just to indicate that I would prefer to watch something that deals outside of slice-of-life/realistic scenarios. I have literary fiction for that.

Series:
FLCL was pretty fun very short anime about growing up that did somehow end up in. (6 episodes)

Noir was pretty awesome series about an assassin

Ebichu the house keeping hamster is the most hilarious thing i've ever seen ( I believe it's still available on Youtube with some amazingly comprehensive subs)

Golden Boy is a short series that is hilarious if you can identify with a young sexually frustrated guy.

Movies:

TOKYO GODFATHERS Probably the best anime i've ever seen especially for people like yourself. It definitely touches on almost all of your sucker categories and touches nothing from the dislikes. If you try only one thing in my post it should be this.

Howl's Moving Castle
Princess Mononoke
Spirited Away

The Miyazaki Trio. You have to see these. Really any of these Stuido Ghilbi/Disney releases. They are sometimes hit and miss or feature things you dislike but I have similar likes and dislikes and have only been disappointed by one.

Well then, sorry if I seemed aggressive. It's just so many qualifications.

My two favorite:

Lupin the 3rd: It's about a guy who steals stuff. His sidekicks are a guy with a gun, a samurai, and a hot chick. By the premise, it's sounds "meh" (especially with the way I described it). But it has a lot of humor, some decent action, and just...it's funny.

Case Closed: Words can not describe how addictive this show will become with you. It's about a guy who is transformed into a kid and solves murder cases. But the episodes are told in the most suspenseful manner. The axe-murderer episode was freakin' scary.