On PvE servers you will only be able to fight against other players in designated arenas.

PvP - Player versus Player
While Age of Conan has much to offer PvE players, many have been drawn to the game for its true PvP experience. On PvP servers players may kill NPCs, but they may also kill each other. For this reason, your travels become far more dangerous. In addition to keeping an eye open for NPCs, you must also watch for other players, which can at times become quite tricky due to the "Hiding" skill. Some players can remain hidden and seemingly come out of no where. PvP players must remain alert at all times. Upon your death you will receive a temporary decrease in stats.