Hear me out, I know when you hear the word "anime" you think "oh, that weird, gay, Japanese cartoon stuff?" let me break it down, weird? yes, almost always, but in a good, well thought out, well scripted, beautifully drawn, interesting creative way. japanese? almost always, I'm not even sure if it can be considered anime if made outside of japan. cartoon? no, ANIMATED SHOW I think would be a more correct terminology, most animes have gratuitous amounts of more depth, character development, plot, and violence or sexual themes you wouldn't find in what we know as "cartoons", gay? no...at least not the anime's I've seen, literally or figuratively. but hey, I'm sure theres a few out there.
So heres a list of different animes, a rough outline of their story, and the reasons why they are amazing shows.
deathnote: this anime was surprisingly dark to me, even after watching claymore, which was probably why I liked it so much. this anime has the best plot twists and scripting I've seen in an anime thus far, while it's not much "action" there is alot of killing that goes on, and I actually learned to love the slower moving episodes. every episode kept me wanting more, and I was on edge the entire series.
cowboy bebop: you may have heard of this one, It's a little older than the others, but when it hit, it hit big, I mean this show was big in the U.S. when anime's weren't even popular. it follows a couple of bounty hunters that go around the galaxy chasing bad guys in thier spaceship. some like to compare it to the show "firefly" in terms of genre, and while it does have that "space western" feel, I think its a very original show, and worth watching every episode.
fullmetal alchemist: I wouldn't recommend this as a first anime if you've never watched one before, just because its got some strange concepts that you may not be used to. It has a strong storyline that lasts for many episodes and I think is still being produced, It follows two brothers that are on a search for a way to bring their mother back, theres lots of cool aspects of this show that are kind of superpowerish, but set in a more medieval place.
darker than black: I will be honest, I still don't understand this show 100% but thats because it is so flippin rich in its storyline. this show has really cool people called contractors that basically have different supernatural abilities, but the all have to pay a price for these abilities...ooooooo...mystical and stuff. anyways, if you want a show thats set in a modern day city atmosphere thats got great depth and a protagonist you will grow to love, watch this.