Action
Films in the action genre will usually include high energy scenes (like fights, escapes or car-chases). An example of this is 'Thor: The Dark World' and 'The Hunger Games'. Both of these films are high-budget and include fights or battles, all these aspects fit into the action genre.
Adventure
Adventure films are a lot like action films as some movies can fit both genres. Like 'Thor: The Dark World' can also fit into the adventure genre. Adventure films are usually exciting stories. Another film that fits this genre is Monster University.
Comedy
Comedies are used to introduce laughter. Films which fall under this genre will contain a lot of comical events. This type of film is likely to mix with other genres, romantic comedies and comic horror for example. An example of this is "We're The Millers", which is about a drug dealer who gets certain people to pretend to be his family in order to succeed in drug smuggling.
Crime
From the genre title it's fairly obvious that Crime films include crime. These may have been committed in the past or present times. Films in this genre can often be linked to 'Action' and 'Adventure' films.
'Dispicable Me: 2' is a child-friendly example of this. In this film Gru and his minions are on a mission to save the world.
Fantasy
Magic or supernatural powers are often present in fantasy films, these are used rather than technological abilities. Examples of fantasy films can be shown in the form of the Harry Potter series, in which witches and wizards have to fight the dark magic attacking them.
Historical
An example of a historical film is 'Schindlers List' which is about the concentration camps set up by Hitler. Films which fall under this genre are factual and tell stories from the past, these are usually significant points in time.
Horror
Horror films create tension and are used to frighten the audience. These films can also be linked to the comedy genre (for example 'Zombieland' and 'Shaun of the Dead'). Films like 'Jaws' are supposed to make the watchers jump and scare them.
Mystery
'The Others' and 'Hot Fuzz' are examples of mystery films. Movies put in this genre often creates a unknowing tension. It's usually the end of the film which uncovers vital information to make everything more understood.
Romance
Films like 'Perks of Being a Wallflower' fall into the romance genre. 'Perks' is about a boy who's had a hard life (abused as a child, best friend committing suicide), but then he meets Sam and falls in love with her. Romance films are usually about two people falling in love.
Sci-Fi
Sci-Fi films usually show fiction fantasies which can't be applied to real life. 'The Worlds End' shows this.. In this film a group of old friends go on a pub crawl but end up fighting of being turned into inky-monstery things. The generic sci-fi film would include extra-terrestrial species,space-crafts and time travel.
Thriller
Films in this genre will often create a feeling of suspense, tension and excitements. These tend to produce a lot of adrenaline. One film which follow these factors is 'The Hunger Games: Catching Fire', in this film the tributes are faced with life-threatening factors such as poisonous gas and dangerous monkeys.
War
War films, obvious from the title, are usually based on warfare. They are often historical or fictional. A few films which fall under this title are 'Saving Private Ryan' and '300'.
Western
Usually based on stories from American Old West in the late 19th Century, most western films portray the conquest over the wild. Films which are in this genre include 'The Lone Ranger' and 'Django Unchained'.
Although there are many more film genres i believe these ones to be the most popular and therefore more important to understand.