Teleportation was a term for traveling from one location to another almost instantaneously. Numerous advanced cultures had this capability through the use of transporter technology. A device facilitating teleportation might be known as a teleporter.
The Q were capable of teleportation. (TNG: "True Q")
There are a number of instances of advanced beings being able to transport things and beings from one place to another, instantaneous and without transporter-like visual effects. These capabilities were not explained to be the result of advanced transporter technology and might be considered teleportation even if that term was not used. Examples include the master thrallGalt of Triskelion who was able to teleport himself, and Armus of Vagra II which was able to teleport things from one place to another but limited to the surface of the planet.
In the script of TNG: "When The Bough Breaks", it was explained that each room on Aldea had a "Teleporting Arch" through which people could move from place to place on their planet simply by stepping into it and stating their destination. In the finished room, the Aldeans still used a beaming-like technology to go enter and exit rooms, but no teleporting arch as such was featured.