As of 2378, there are 40 some occaisions noted by the UFP of
Time Travel.
In the
25th century, time travel was mostly possible but still risky
As of the
26th century,
historians and
anthropologists used
time-pods to travel through time to observe historical events.
In the
29th century, the Federation had the ability to scan time as well as space, and travel back (and presumably forward) in time to attempt to fix issues and anomalies.
In the
31st century, time travel was commonplace. Federation temporal agents from this time became involved in a
Temporal Cold War, which eventually led to
temporal wars. After these wars, time travel was banned and the technology used to travel in time was destroyed.