I watch a fair variety of anime genres, but I suppose a lot of the ones I love are either really action-packed or no action at all. I'll try to only recommend those that haven't been stated (unless I really freaking love them lol).Clannad
and Clannad: After Story
Get the tissues ready!
A pretty short series... but wow. I'll remember these characters forever. It presents itself as an action anime, but you'll start to see it's really all about the story. It starts of with a guy named Otonashi and little does he know, he's dead. He's trapped in this strange universe where everything seems normal, but a little too normal. He comes to make a few friends who are in the same predicament as he is and they go on quest together to find purpose and reasoning to their lives/deaths. Really, really awesome but once again, get ready for some heart-ache.Shingeki no Kyojin (Attack on Titan)
Currently one of the most popular animes/mangas right now, and I have to say, it is really freaking amazing. If you want to see storytelling and action done right, then I would full-heartedly recommend this. I don't want to ruin anything so... you'll just have to watch it for yourself. You really don't know much more than the main characters, so you'll come to learn more about their world just as they do.Free!
Okay, honestly, as a straight male, I found this anime to be... my guilty pleasure. LOL
It's only on the first couple of episodes right now, but you kind of just learn to love the characters and swimming. Oh my gosh, this anime will make you want to go swimming so bad you don't even... lol
Basically a story of a group of young girls that come together to form a band and it really just goes from there. Not sure how else to explain it, but it was really good!Tsuritama
A great story about friendship that consists of a group of teenage boys (and a few aliens) that have a passion for fishing. The first few episodes probably won't make any sense, but once the story starts to develop, it gets much better. The Devil is a Part-Timer!
The devil, or Satan, is forced to retreat after his realm has been taken over by humans. Little does he know, he comes to modern day Japan, a land where even demons take human form! Satan and his servant Alciel come to learn how to live/make a living in the human world. It's a great little comedy that's not afraid to poke fun at the everyday problems and struggles of the adult life.