The title says it all: Which starship has travelled back in time the most number of times? The only restriction is it must be from canon. It can be from any society (not just Starfleet or Federation), any time period.
The Enterprise-D seems to be the winner here.
In the episode TNG: Cause and Effect the Bozeman and the Enterprise both travel back in time four times.
The original USS Enterprise...
According to this list of time travel episodes, the original Enterprise travels back in time 4 times:
- Once in 'The Naked Time' (to three days earlier)
- Twice in 'Tomorrow is Yesterday'
- Once in 'Assignment Earth'
...and the USS Bozeman
which travelled back in time 4 times during the course of TNG 'Cause and Effect (kudos @Richard)