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Would you need a power source? If you aim your ship correctly, then put everything alive into cryo, the ship could go completely dark, vent all heat and become a frozen rock. Then after [very long time] the ship enters the vicinity of a different star and can be reactivated and unfrozen using solar energy. You dont need energy to maintain cryo if the whole ship is at 1° kelvin.
(Of course that relies on cryo sleep being possible)
Or synthetic life. (Robots)
Only if they can be turned off (same as the cryo sleep). The whole ship either has to have enough energy to last potentially 100000 years (no theoretical power source exists like that) or enter a state of 0 energy consumption. Solar/radiation collectors dont work if you are to far from a star. Synthetic life still needs energy
Well, that depends on how far you're going. If you pick a nice close target, let's say 3 light years away, you can potentially get there pretty quickly. With fusion propulsion systems you could make the trip is something like 70 years, coasting most of the way. I'd need to check the math to get exact numbers, but I recall fusion allowing for pretty reasonable trip times.
But if you can survive for hundreds or thousands of years, then solar sails become an option. Then it becomes a materials science problem of how thin can you make a sail that will still hold together. The greater the sail to payload ratio, the faster you go.