Well, I'm not as big an anime fan as I used to be, but I think I understand the problem. A lot of the "big" series intended to occupy long term spots on TV like Bleach, Naruto, Dragonball, etc... tend to involve tons of filler because they are something people tend to get into as part of a routine, and it's set up where missing an episode or two isn't likely to be a big deal. This becomes more noticeable if you sit down for a few hours for some video entertainment as opposed to seeing it spaced out over a period of time. Now that Anime is better known, the novelty of it and it's unique tropes don't carry things so well. I get the impression from things I've heard that "Attack On Titan" was probably conceived as a show in that vein but for various reasons it might not peak out that way.
That said, I think one of the big problems with Anime is that attempts at drama and more serious storytelling don't always pan out because of localization issues... and yes, fan translations can be better than professional ones, in part because the fans just sit down and do it, and are motivated to do it right for reasons of love (though this is not always true), the pros drag their feet instead of planning for immediate localization, and then when they finally get around to it, it seems the people they get have a sort of "why bother" attitude, especially if someone else already did a version as accurate as anything they could turn out.
I think series like "Higurashi: When They Cry" (basically an anime-horror version of Groundhog's Day, where you have a few episodes of nothing much happening, followed by a massacre and a reset) never caught on, because they were so heavily dependent on translating a drama without a whole lot of frequent action to tie things together, not to mention that a lot of it is a mystery and certain hints or things that are supposed to make you wonder can revolve around something as simple as a turn of phrase.
That said while it's a mixed bag there are a number of Anime series that I think do well at not having a huge reliance on drama and a lot of stuff going on so things happen in each episode.
Outlaw Star
Escaflowne
Gantz
The Dirty Pair (just about everything)
Coyote Ragtime Show
R.O.D. (Read Or Die)
Fushigi Yuigi: The Mysterious Play (and it's sequel)
Revolutionary Girl Utena (the series, the self contained movie is even more surreal and works best if you see series 1st)
Gundam W
Gundam Seed (less impressed with it's sequel)
Noir
Baccano
Deadman Wonderland
Dagan Rompa
Spiral
Dual
Lost Universe
Ruruni Kenshin (the TV comedy series, not so much the Samurai X stand alones)
Rune Soldier
Soul Eater
Soul Hunter
Hellsing
Bubblegum Crisis 2040
Corpse Party (anime viewable on Youtube still I believe)
I could go on, this is a mixed bag, ranging from truly surreal comedies, to the fairly serious. I don't want to post a huge message full of nothing but titles (as my messages tend to be long enough). While a lot of those series might have a filler episode or two (the cast goes to a hot spring!) they generally stay on target and have things happen to move the story forward in pretty much all the episodes and/or do episodes with a self-contained plotline. "Ghost In The Shell" (two seasons) is an example of a series that does both "metaplot" episodes and ones that are self contained representing other cases the cyborg police get involved in outside of the main plot (since the world doesn't stop) and need to be dealt with.
To be honest my problem with Anime oftentimes revolves around terrible endings, many of which can actually be worse than the end of "Mass Effect 3" and that can take some doing.
I'll include an honorable mention for "Hell Girl" which is kind of grim, but pretty much every episode is self contained. It's basically about a demon people can summon and sic on other people to take them to hell, but in return when they die they go to hell themselves. So pretty much every episode ends with everyone being doomed to eternal agony, though whomever summoned The Hell Girl usually has things turn out a bit better for them on earth for a bit. It follows a pretty standard formula (bad stuff happens, person calls Hell Girl, is shown that the cost of justice/revenge/setting things right is going to hell, the person usually refuses, things get worse, hell girl is called again, unholy vengeance is wrecked on the tormentors, and things get better for the summoner but they are also equally doomed). I could personally only take so much of a series where nothing good happens to anyone, ever, I mean even the demon seems perpetually depressed and unhappy with her job.
