Every OpenArena player or server admin should have clear the concepts of the basic game options, meaning those "server" variables which control the fundamental rules of a match, and which can be summed up as Gametype, Fraglimit, Capturelimit and Timelimit.
Other than these, there are many other options which allow to customize a match experience in many ways (e.g. automatic regeneration, instant-gib, spawn protection, etc. etc.). There is a dedicated page for them: Special game options, don't miss it!
Each "gametype" is an independent set of rules to play the game, with different goals: in some, you just have to "frag" (kill) your opponents, in others, you have get a flag and bring it to a certain "base", etc.
Gametypes are divided into "team-based" and "non-team based". Gametypes are controlled by /g_gametype <number> variable, which default value is 0 ("Free For All").
OpenArena has got many more gametypes than the original Q3A game, see Gametypes page for the complete list. Mods may have their own gametypes, so you should check each mod own documentation. "G_gametype 2" is a special gametype used in Single Player Deathmatch mode only, which should not be used for online gaming.
Some game modes do have some gametype-specific options which are not listed here nor in Special game options page, but in pages dedicated to that particular gametype (e.g. Elimination page lists the variables which allow set the initial load of weapons for that mode and its related ones).
Some servers allow users to vote to change gametype, but it's not so common, also due to breaking map rotation scripts. It has been this way since the original Q3A game. Auto change map feature -requires OA 0.8.8 or later- does not have this problem.
"Fraglimit" is a variable used by some gamemodes to set the score players or teams are tasked to reach in order to win the match; usually indicates the number of kills required. The variable is simply fraglimit <number>; setting it to 0 means "no limit". The HUD shows that limit, if set. If both fraglimit and timelimit are set, the first one reached ends the match.
Default value is 20; often used values range from 10 to 40.
Server admins can allow to vote to change fraglimit, optionally setting g_voteMaxFraglimit <number> and g_voteMinFraglimit <number> variables to place upper/lower limts to the values allowed to vote.
"Capturelimit" is a variable used by some gamemodes to set the score players or teams are tasked to reach in order to win the match; it may indicate the number of flag captures, or individual "rounds" won, or the time specific points have been owned. The variable is simply capturelimit <number>; setting it to 0 means "no limit". The HUD shows that limit, if set. If both capturelimit and timelimit are set, the first one reached ends the match.
Default value is 8; often used values are near to that, with the exception of Domination mode which requires higher values, such as 300.
Currently (OpenArena 0.8.8), server admins can allow to vote to change capturelimit only by setting up custom votes.
"Timelimit" is a variable which specifies the time (in minutes) a match should end. The variable is simply timelimit <number>; setting it to 0 means "no limit". If set, players will hear a couple of audio warnings before the time runs out. If both timelimit and fraglimit/capturelimit are set, the first one reached ends the match.
Elimination and similar modes do also use elimination_roundtime <number> (in seconds) each individual "round" should last.
Server admins can allow to vote to change timelimit, optionally setting g_voteMaxTimelimit <number> and g_voteMinTimelimit <number> variables to place upper/lower limts to the values allowed to vote.