Odamex supports a fair share of the essential game modes offered by the FPS genre:
Free For All
Free For All, otherwise known by its acronym as FFA or simply deathmatch (DM), is a game mode that supports up to 16 players at once where the objective is to attain the highest amount of frags and reach the set fraglimit, facing the other players. It is the most basic and played game mode.
Head to Head
If you'd like to be given a break and shift your focus from fighting a plethora of players at once onto battling a single individual, then Head to Head would be the perfect choice. Head to Head, commonly referred to as 1-on-1 or duelling, is a variant of deathmatch where the amount of players playing simultaneously is limited to only two, hence the name "Head to Head". The objective is the same -- to rack up the highest quantity of kills, yet only against one adversary. This game mode particularly allows for high competition among individuals and many tournaments center on this game mode.
Team Deathmatch
This is the ideal game mode if you would like to still fight a horde of players yet have some allies back you up. Team Deathmatch is a team-based variant of deathmatch where players are divided into teams determined by color; traditionally blue and red teams. The goal is overall the same, yet a whole team must achieve the highest amount of kills while facing the opposing team.
Capture the Flag
A highly popular and addictive game mode, Capture the Flag draws attention to strategic team-based gameplay. Capture the Flag, like Team Deathmatch, is a team-based game mode, where two teams that are determined by the colors red and blue fight each other. However, the objective does not pertain collecting the highest quantity of frags. Each team has a base with a flag in it that is of the same color as the team to which it belongs (e.g. the red flag belongs to the red team). One team has to capture the flag of the other team while it is still in possession of its own flag (e.g. the blue team has to capture the red team's flag while it still has its own flag and vice versa). Then, the team has to bring the flag to its base to where its own flag is in order to score a point (the blue team takes the red flag and brings it back to its own base to where its own flag is situated to score). If the team's flag had already been captured, then it cannot score until its flag had been returned (if the red team had already taken the blue flag while the blue team has the red flag, then the blue team cannot score unless its flag is returned and vice versa). To return one's team's flag, the person who is holding the flag has to be killed.
Cooperative
If going against other players isn't your style, then you can always battle against the monsters with other players on single-player maps. 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 acquired on that same level, unless the server has such settings that allow for players to keep their keys, items, and weapons upon respawning. 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.