A few protoss are known to possess this ability, such as Tenarsis and Khyar. The preserverZamara was able to peer into time and gain glimpses of the future.Zealots are also able to use a limited form of precognition that allows them to predict enemy movements, allowing them to avoid enemy attacks.
A number of terrans have displayed precog abilities—Octavia Bren had premonitions about what the future would bring in an emotional sense (a 'bad feeling') while Delta Emblock had precognitive abilities made manifest in her dreams. This ability allowed her to avoid being kidnapped by Project Shadowblade.
At least some xel'naga possessed precognative abilities, indirectly predicting the events of the Great War and recording another prophecy, stored in artifacts which were later discovered by the protoss adventurer, Zeratul.
↑And alone, floating on a dark platform above the burnt-out planet of Char, Sarah Kerrigan, the Queen of Blades, sat and lorded over the ravenous Swarms. Unable to shake the feeling that a great threat loomed just over the horizon, Kerrigan could only stare off into the vastness of space where she beheld a great void. Or perhaps a reflection of a hollow victory and of the trials yet to come... StarCraft: Brood War. Vivendi Games. Level/area: Epilogue (in English). 1998.