Mystery - Anime Genre that keeps the views wondering whats going to happen next, usually involves a chain of unexplained events, where the protagonist tried to solve them. Normally with an above average intellect the protagonist slowly encompasses himself in the mystery and often becomes obsessed with the case. Example: Death Note
Psychological - Like mystery it keeps you on the edge of your seat wondering whats next, but there is always an additional twist. Although it goes hand in hand with the mystery genre, psychological anime tends to leave the viewer guessing till the very last moment about what will happen. Example: Zankyou no Terror
Samurai - Often (if not always) used with the historical genre with the time frame being centered around the Edo Period in Japan, often has alot of action although the element of drama is also seen due to the time setting. Example: Gintama
School - Often (if not always) used with the historical genre with the time frame being centered around the Edo Period in Japan, often has alot of action although the element of drama is also seen due to the time setting. Example: The Melanchony of Haruhi Suzumiya
Sci-fi - Very often incorporated with the fantasy, mecha and space genres.Also often includes alien creatures and to some extent giant monsters or robots. Example: Parasyte the Maxim
Seinen - Is basically an indicator of an anime aimed at the adult male (ages 18-40). They tend to usually be psychological, sexual and violent while dealing with character development and relationships in a very mature way. Example: Cowboy Bepop