A sensor representation of a temporal rift.
A tear in the fabric of spacetime, a temporal rift is a highly dangerous temporal anomaly. There have been numerous encounters with such rifts, in many cases, the vessel making the encounter has been transported through space and time.
The USS Bozeman entered a temporal disturbance in the Typhon Expanse in 2278, and travelled to the year 2368, where it collided with the USS Enterprise-D and started a temporal causality loop. (TNG: "Cause and Effect")
The Enterprise-D encountered a temporal rift-like phenomenon in the region of Archer IV in 2366. The rift was identified as a Kerr loop formed from superstring material. Such a structure requires high-energy interaction in a small area of space in order to be formed, such as the detonation of a volley of photon torpedoes. Although sensors seemed to register a vessel emerging, readings quickly vanished, and the phenomenon collapsed shortly after.
A temporal rift.
The rift had, in fact, transported the USS Enterprise-C and its crew from 2344 and the Narendra system. The disappearance of the vessel from its proper place in time caused the formation of an alternate timeline, which was resolved by taking the Enterprise-C back through the rift, leaving no direct evidence of the temporal upheaval. (TNG: "Yesterday's Enterprise")
The creation of artificial temporal rifts allowed certain 29th century Starfleet vessels to travel through time. The Aeon used a temporal rift to travel back to 2373 in order to destroy USS Voyager. When the rift destabilised, both Voyager and Aeon were pulled in by the gravimetric forces, ending up in the 20th century. (VOY: "Future's End" and "Part II")