I don't have A particular favorite, I have several ships I love; but one of them surely is the Heart of Gold.
Powered by the unique Infinite Improbability drive, the ship travels by having the ship's computer calculate precisely how improbable it is for the ship to -be- in the desired location and feeding it into the engine, the matchbox-sized, eponymous Heart of Gold - which itself only exists because someone had a finite improbability calculator work out how improbable it was for something like it to exist. The genius of the move led to the death of its creator when he was lynched by outraged scientists who hadn't thought of it before.
There is, in practice, nothing the ship can't do and nowhere it cannot go, since, in principle, nothing is truly impossible; just improbable to a varying degree.
Unfortunately the side effects of having something in your ship that makes literally any concept a possible reality are unpredictable (at least without the ship's computer) and lead to some peculiar situations.