Survival of the Fittest: A 'free-for-all' mode where each player gets points for killing each of the other players. Whichever player has the most kills or 20 kills at the end of the match wins.
Civil War: Similar to 'Survival of the Fittest,' but in this mode players are divided into two teams and the team with the most collective kills at the end of the match wins.
Last Splicer Standing: A variation of 'Civil War' in which players do not respawn after being killed. Each match consists of several rounds in which players attempt to outlive the players on the enemy team.
Capture the Sister: A 'Capture the Flag' style mode where players are divided into two teams. One team has to protect a Little Sister while the other team tries to steal her and place her in a vent on the other side of the map. The team protecting the little sister will have a randomly chosen player be a Big Daddy. After a pre-determined amount of time, the teams switch roles. Whichever team has the most captures at the end of the match wins.
ADAM Grab: In this mode there is one Little Sister on the map and the player must seek her out and maintain possession of her as long as possible. The first person to hold onto the Little Sister for 3 minutes wins.
Team ADAM Grab: A variant of 'ADAM Grab' where players are divided into two teams. The objective is the same, but victory is determined by a collective score rather than individual scores, and the first team to hold the little sister for 5 minutes wins.
Turf War: Players are split into two teams and each team must reach pre-determined points on the map to capture that point. The team with the most control points over the longest time wins.
taken from the wiki:
http://en.wikipedia.org/wiki/Bioshock_2
