Death match (DM)
Death match is an all out frag fest, there’s really nothing else to it.
The game ends when the time limit or frag limit has been reached.

Team death match (TDM)
Team death match is the same as death match except there are 2 teams and the frags are combined.
The game ends when the time limit or team frag limit has been reached.

Domination (DOM)
In Domination the player’s team must capture and hold as many flags as possible by standing near the flag.
The game is won when a team captures all the flags or the time limit is reached.

Sabotage (SAB)
In Sabatoge each team has an object they need to protect from the enemy and must also plant a bomb on their object. There is only one bomb and this player is marked for everyone to see.
Sabatoge is won when your team plants and defends the bomb against the enemy.

Search and Destroy (SD)
In Search and Destroy the attackers carry a bomb(s) to two plant points and must defend against the enemy. The defenders must stop the attackers.
Search and Destroy is won when the attackers are eliminated or the attackers detonate the bomb.

War (WAR)
War is similar to Domination but only one flag can be contested at a time as each team pushes into the enemy base.
War is won when a team has captured all the flags.

King of the Hill / Headquarte (KOTH)
King of the Hill has both teams scrambling to hold a radio that is randomly placed around the map.
KOTH is won when a team has reached the score limit, points are added for length of time radio is held.

Capture the Flag (CTF)
Capture the Flag has both teams defending their flag and trying to capture the enemy’s flag.
The game is won when a team has reached the capture limit.

Sources: Wikipedia Modified by Fanterazzi