Here's some great anime. My favorite anime genres are action, comedy, and romance, so that's pretty much what's in here. Note that most of these are based off of manga.
Noragami -
"A minor god who doesn't receive any attention tries doing odd jobs to earn respect!" Plus, it has a sick-ass opening theme!
Action, Adventure, Thriller, Comedy, Semi-Romance
Cowboy Bebop -
"Enter a world in the distant future, where Bounty Hunters roam the solar system. Spike and Jet, bounty hunting partners, set out on journeys in an ever struggling effort to win bounty rewards to survive." If you're looking for a gritty sci-fi with tons of badasses, this is your top pick. (It's about 15 years old but it's aged well.)
Action, Adventure, Comedy, Drama
Soul Eater -
"Set in the Shinigami technical school for weapon meisters, the series revolves around 3 groups of each a weapon meister and a human weapon. Trying to make the latter a "Death Scythe" which is the highest title for a weapon and thus fit for use by the Shinigami, they must collect the souls of 99 evil humans and 1 witch." More amazing soundtracks, but a little dark if you're into that kind of stuff. (Not R-rated, mind you.)
Comedy, Fantasy, Action, Supernatural
Durarara!! -
" In Tokyo's downtown district of Ikebukuro, amidst many strange rumors and warnings of anonymous gangs and dangerous occupants, one urban legend stands out above the restâthe existence of a headless "Black Rider" who is said to be seen driving a jet-black motorcycle through the city streets." It doesn't make sense at first, and won't until around the fifth episode or so, if you have the patience. One of the best plots in an anime ever.
Mystery, Action, Supernatural
The World God Only Knows (All three seasons) -
"Keima is a dating sim champion. Cute girls are rendered powerless by his irresistible game playing techniques. Too bad things aren't that way in the real world. That is, until his tempting game playing causes a real live—and very bubbly-cute—demon hunter named Elsie to materialize! Now Elsie wants Keima to help her free hot girls from sneaky demons who secretly possess them. " If the plot sounds stupid, watch it anyway. This is seriously my favorite anime.
Harem, Comedy, Romance, Supernatural
Hunter x Hunter(2011 version) -
" A Hunter is one who travels the world doing all sorts of dangerous tasks. From capturing criminals to searching deep within uncharted lands for any lost treasures. Gon is a young boy whose father disappeared long ago, being a Hunter. He believes if he could also follow his father's path, he could one day reunite with him. After becoming 12, Gon leaves his home and takes on the task of entering the Hunter exam, notorious for its low success rate and high probability of death to become an official Hunter." This is the best action series ever. Watch it. No, really. It has 120 episodes and counting, though...
Action, Adventure, Super Powers
Nisekoi -
"Raku Ichijou is an average high school student. He also happens to be the sole heir to the head of a Yakuza Family called the Shuei-gumi. Ten years ago, Raku made a promise... a secret promise with a girl he met. They promised one another that they will "get married when they reunite". Since then, Raku never let go of the pendant the girl gave him." It's not even finished, but I read the manga and I love it. Yes, it's a harem. Yes, it's silly. Yes, I love it. (Onodera ftw)
Romance, Harem, Comedy, Drama
I'll add more later, this took forever to type.
