Odamex supports all of the basic game modes offered by other popular online source ports:
Free For All
Free For All is a term given to deathmatch in which the goal is to kill, or frag, as many other players as possible. The match will end when either someone reaches the fraglimit, or when the allotted time runs out. Killing yourself results in a deduction from your total frags.
Head to Head
Head to Head, commonly referred to as 1-on-1, is a variant of deathmatch where the key characteristic is that there is a maximum of two players playing simultaneously. The dynamics of head to head games are much different than that of a standard free-for-all, because all of the players' attention is directed toward one individual, as opposed to many. Typically, this makes for a much slower-paced game and invokes players to make careful decisions about what to do next.
Team Deathmatch
If you want a break from the usual free-for-all's, and don't really want to get into the complexity of capture the flag, then Team Deathmatch is always an option. Like normal deathmatch games, the goal is to accumulate the most frags, but the climax of this plot is that you have a helping hand. The match will end when a team's total frag count reaches the fraglimit, or when the alloted time runs out.
Capture the Flag
Capture the Flag, like team deathmatch, is a team-based game mode where the goal is to take the opposing team's flag and bring it back to your own. Successfully doing so results in a capture thus adding to the team's score. The game will end when a team reaches a specified number of captures, or when the allotted time runs out. Unlike other team modes, different types of strategies (?) tend to surface in capture the flag, that are formed to help maintain balance in the game. Defense and offense are considered two of these and are pretty self-explanatory.
Cooperative
If going against other players isn't your style, then you can always battle against the monsters with other players. In cooperative games, players work together to complete the level and any existing subsequent ones. When a player dies, he or she starts back at the beginning of the map without any keys, items, or weapons he or she may have accumulated during that level. Since players are not the target of other players, it is worth mentioning that all players are visible on the automap and can even see "through the eyes" of other players.