An artificial intelligence is a machine which demonstrates the ability to act independently, form its own conclusions and make a suitable response.
The Vulcan Science Academy did some research in the development of artificial intelligences during the time of the Sundering. It was this research that was consulted by the Technocrats within the Vulcan-in-Exile fleet as a force multipler amongst the Great Ships in order to help ease the strains they were facing. However, it was a controversial view amongst the Adepts of Mount Seleya who believed that a possible fusion of the mental arts would be combined with technology which was blashpemous in their eyes. (TOS - Vulcan's Soul novel: Exiles)
During the Occupation of Bajor, the Cardassian Union used Doctor Daul Mirosha of the Bajoran Institute of Science to develop an artificial intelligence in order to aid productivity of the Gallitep labor camp. Once the resources had been used, it was planned for the AI to be deactivated and the Bajoran workers culled. After learning of this, Doctor Daul attempted to aid the workers but ended in a fight with a Cardassian guard and during the struggle, the housing for the AI was destroyed. (ST - Terok Nor novel: Night of the Wolves)
In 2347, Cardassian scientist Cren Veruda developed a computerized artificial intelligence which Starfleet sought to keep from the Cardassian military. To that end, a covert operation was conducted on Kora II to remove the artificial intelligence from Cardassian space. The Borg attempted to obtain Veruda's AI in 2369 at Uridi'si. (DS9 - Mission Gamma novel: Lesser Evil)
Romulans are known to routinely check their Rokhelh software to determine whether their artificial intelligences have developed self awareness. Should such a matter occur, the Romulans were known to purge the affected systems. (TTN novel: The Red King)