Hey JZ! I'm a relatively major fan of anime myself. The recommendations below are fairly well-known and popular among a lot of viewers. Definitely check them out!
So, here goes! In no particular order!
1. Death Note
A high-school boy, Yagami Light, discovers a supernatural notebook that allows him to kill anyone by simply writing the victim's name. He then begins to exterminate all the criminals and 'useless' people from the world, in hope to make it a better place. But soon, his suspicious actions are captured by the world-famous detective known as codename: L. Neither of them know each other's identity, but both of them are determined to get rid of each other.
I haven't seen this one yet, but they say it's pretty good. Yes, there are three 'O's.
Basically, Ryouta Sakamoto wakes up on an island, with no idea how he got there. The last thing he remembers is playing the game Btooom on his computer, of which he was the best player. Soon, he learns that the only way to escape is by being the last competitor alive in this real, wicked game of Btooom.
3. Code Geass
When Britainia defeated Japan in the wars, and Japan was renamed Area Eleven as reminder of their failure. After ten years, a high-school boy named Lelouch becomes the leader of a rebellion group named The Black Knights to overthrow Britainia. What makes this protagonist special is his mysterious power named Geass, which allows him to control people's actions. The story revolves around Lelouch trying to form peace between nations, AND finding out who really murdered his mother.
4. Fairy Tail
Incredibly popular one. Don't get fooled by it's name; the anime isn't about fairies or happily ever afters.
In an imaginary world, the Earth Land, everyone gets to choose a magical guild. Guild members would battle and defeat creatures of all sorts to improve their magic. Lucy Heartfilia wants to become a full-fledged mage and joins one of the most prestigious Guilds in the world: Fairy Tail. Basically, she becomes friends with many Fairy Tail members and together, they accomplish missions and hardships.
5. Sword Art Online
Haven't watched it yet? Watch it. That's all I have to say.
Hope you have fun!!
P.S. Could the Mods do more character posts on SA? Like when Meilin, Rollan, Connor and Abeke post their own...posts? Pleeaaase? We'll love you (more)!