There are many genres to choose from. Sooner or later, you'll find your favorite! ☺
Action - By far one of the most common genres out there and the name basically explains it all. There is fighting, battles, and action stuff. Example: Naruto
Adventure - As the name says, it involves with characters moving around and exploring new places. These anime tend to be very long, but the characters typically have a solid quest. Example: Fairy Tail
Bishounen - A young male whose beauty exceeds gender somewhat and is mostly targeted to girls. Basically, pretty boys. Example: Ouran High School Host Club
Comedy - As its name implies deals with humour. And well, just funny stuff. Example: Amagi Brilliant Park
Demons - Pretty common genre, deals with evil spirits, demons, witches etc, normally combined with the action. Example: Black Butler
Drama - Suspenseful, shocking and full of emotion. Characters and the plot are well developed and great view of events. Example: Death Note
Ecchi - This is like the PG-13 of anime. It shows some sexual stuff, but not so much that you will have to bathe in holy water. Example: Astrotte's Toy
Fantasy - Magic worlds, magical powers and monsters, these are the main components that make up fantasy anime. Example: Blue Exorcist
Game - As the name says, it basically involves the characters playing some sort of game. Or they are in a game. Example: Sword Art Online
Harem - When the main male character is surrounded by female characters. Example: Astarotte's Toy
