Children's. This is pretty self-explanatory. Generally age two up to around eleven. They tend to have pictures and a moral of the story. Sub-genres: Picture, middle-grade, early childhood, traditional, pop up and more.
Fantasy. This is very general. Fantasy has at least one element that is not known to be "real" Whether that be the setting, a character trait, or everything. Good characters usually prevail in the end. Sub-genres: alternate world, celtic, christian, contemporary, dark, erotic, epic, historical, medieval, mythic, romantic, science fantasy, series, urban, and many many others.
Horror. This is pretty self explanatory. Ending varies between protagonist winning or unknown. Tends to be high anxiety and edge of seat read. Sub-genres: aliens, cross, cutting edge, dark, extreme, humorous, paranormal, suspense, bizarro and lots of other small genres.
Mystery. There's an unsolved situation, puzzle or murder or crime, that is usually solved by the ending. Usually main character is smart and knows what they're doing. Sub-genres: amateur, caper, cozy, doctor, hardboiled, historical, legal, locked room, romantic, supernatural, whodonit, etc.
Romance. I don't even know how to describe this. There are so many types of romance that a general description isn't suffice. There is love between people and they explore it? Eh. You know what it is. Sub-genres: action, baby love, christian, contemporary, family, gothic, historical, lesbian/gay, paranormal, sweet, time travel, and hundreds more.
Short Fiction. Obviously defined by its length. Could be a novella but generally much shorter. Sub-genres: flash, drabble, pinhead, six word, twitterfic. (I never knew about this genre before.)
Triller(Suspense, Action, Adventure). There are extraordinary circumstances where the good prevails. There is a hero who most of the time wins. Lots of adventure and action. Sub-genres: aviation, conspiracy, disaster, espionage, legal, political, romantic, survivalist, tecno-thriller.
Western. Set between 1800 and 1890, mostly. Most are set, wait for it, in the west! Sub-genres: black cowboy, bounty hunter, civil war, euro-western, gunfighter, mexican, outlaw, quest, revenge, romance, women.
Now, these have been the most common and used genres, in fiction. However there is one more that I must mention. I am probably going to make another post focusing on this genre because it is so new.
New Adult. New adult is the bridge between young adult and adult fiction. Characters are usually between the ages of 18 (sometimes lower) to 25. It is geared towards this age group too. The situations are older and more can happen in these stories. It tends to be a coming of age story. You can really have any sub genre to go along with it.