Kuroko's Basketball 3
With it reaching it's 3rd season currently, Kuroko's Basketball ( Kuroko no Basket ) is an anime based off of the sport of basketball. The main character; Kuroko, is a player with lack of any skill besides passing. With that said, him and his new teammate Kagami, are in search of being the best. Sadly, to be the best, they have to beat members of the 'Generation of Miracles' which Kuroko was a part of. I won't go into much detail, you'll have to give it a go for yourself.
Onto some of the more mainstream anime, Naruto/Naruto Shippuden has always classed as one of the 'Top 3' Anime alongside Dragon Ball Z and One Piece. Naruto is about a young boy who grew up without a mother and a father, he's always striven to be thhe e best ninja and show everyone that he will become the Hokage (leader of his village) and be respected by his fellow villagers. The road get's sketchy when he learns to tame his Tailed Beast which is a power hungry monster sealed inside of Naruto, that amplifies Naruto's strength ten-fold. Definitely a recommendable series.
Yet another mainstream anime, it's all about the title of the show. They're on a search as pirates to find the legendary treasure; the One Piece. The One Piece was left behind by the King of Pirates, Gold Roger and right before his execution he stated that he hid the One Piece; which sent thousands of people to sea in search of this treasure. One of them, being Monkey D. Luffy. See his pirate adventure to find the One Piece and meeting some interesting characters.
This is an anime that more and more people are starting to grasp and realize it's potential. It's all about Ken, a boy who has the power of Rise and he must learn to control himself, because he's not human, and not Ghoul.. he's both. In the beginning of the series, some great character progression was shown as he had to learn how to control himself when going Ghoul because he would try to eat Human Flesh, which is what Ghouls do. This is definitely one of the more interesting series; as it always keeps you on the go.
Sword Art Online
An anime I would recommend to a lot of starters. SAO is all about a young boy named Kirito who becomes one of many gamers trapped inside of the Virtual World MMO; Sword Art Online. You have to make it to the highest floor, and defeat all of the bosses; in order to leave the game. Even with that, there's a catch. If you die in the game, you die in real life.
High School DxD
High School DxD is about a kid named Issei who has been in love with a girl at school, not knowing she was a Demon. Issei had a hidden power that he had never known about, making him attract Fallen Angels who tried to kill him. The girl he was in love with, Rias Gremory; took him into their club and Issei became a demon. The storyline is great in my opinion. Nudity is also in this series, so watch it... alone.
A new season of High School DxD is scheduled for release next month. ( April 2015 )
Hunter x Hunter
Preferably the 2011 part of this series, though both the 2011 and 1998 are good; Hunter x Hunter is a story about young boy named Gon, who has a dream of becoming a Hunter, not to be rich, not to be powerful, but solely to find his father who left him when he was a baby to become a Hunter. His dad became a hunter at the same age Gon did, and it leads to an amazing tale of new opponents, getting stronger, and struggles... until the end. I, for one, am still hoping for a new season.
Main Character named Yukkii, has a diary that predicts the future. It's a game with the prize pool as becoming God of the world. The current God's time of life is coming to an end so he puts a game into play, kill or be killed. However, every diary has it's own unique ability and it's necessary to watch your back. This is one of the more recent series' that I've watched, and it's definitely a great one.
Seven Deadly Sins
There was once a great kingdom that stood tall and purged evil. It's turned ways from it's original state and there is evil within the Holy Knights that used to fight for the peace. The Seven Deadly Sins is a group of Knights that were framed for the destruction of the kingdom and they're forced to flee the scene and disband. They find each other and as the story progresses, they gain intelligence regarding bringing back their members of the team to save the kingdom from it's horrible state.
An all girls school recruits a guy after believing that they should keep the girls away from guys as much as possible during their school years. They came up with an issue, the females had NO social skills and would never make it in the real world. They bring a very lewd guy to the school who they think has a muscle fetish so that he won't be attracted to the girls. Needless to say, it gets very lewd in this series.
One Punch Man
Are you living under a rock? A hardcore action fest right here. Main character, Saitama has trained for multiple years to the point where he went bald after undergoing 'extreme' daily training. However, he becomes too strong, and loses his interest in fighting as he can beat opponents in a measly one punch, hence the title of the series. Saitama is a hero for fun, until he becomes a professional hero and fights for the protection of others and searches for a worthy opponent. In which he finds? No spoilers. Go watch it.