What makes the most sense (real or theoretical) for energy sources to power large spaceships for thousands of years, not renewable
Fusion is renewable if you are going fast enough.
The Bussard Ram Jet can collect interstellar hydrogen as you travel.
Bussard1 proposed a ramjet variant of a fusion rocket capable of reasonable interstellar travel, using enormous electromagnetic fields (ranging from kilometers to many thousands of kilometers in diameter) as a ram scoop to collect and compress hydrogen from the interstellar medium. High speeds force the reactive mass into a progressively constricted magnetic field, compressing it until thermonuclear fusion occurs. The magnetic field then directs the energy into rocket exhaust, providing thrust.
If you can get it up to a high enough speed, then it can use the scoop from the ramjet to feed the reactor.
However even regular fusion will work for a generation ship or other slow boat. The idea here is that the ship does not thrust once it has been aimed at a target star. So, it only needs store enough hydrogen to power its internal systems for a very long time. This is doable for a reasonably (unreasonably) large ship (1+ km diameter, 5+ km long).
The rocket equation strongly suggests that you need to maximise the mass/energy density of your power plant which also means giving consideration to minimising it's volume to save on containment mass etc... For a long trip you also need a power system that can maintain steady output:
The most efficient technology currently in general use is nuclear fission but the power:mass ratio doesn't remain steady over time, nor does overall power output so not suitable.
Nuclear fusion is currently a near future technology with the potential to be as, or possibly more, efficient as fission. It's input can be increased or decreased on demand, to a point, and it can maintain a steady output as long as the fuel lasts.
Matter/antimatter annihilation is the last word in mass/energy efficiency in terms of fuel but we don't really have enough data to look at the efficiency of a large scale reactor. In theory such a reactor would be similar to a fusion device, controlled variable output with steady production as long as the fuel lasts. One of the major challenges of antimatter is that the fuel for a fusion reactor is inert, antimatter is anything but so any leak is actually a ship wrecking explosion.
In theory you could use a sub-stellar mass blackhole as an energy source, it is also nearly perfectly mass efficient but its output goes up, to quite alarming levels, as it runs out of fuel/mass. If you wanted to use this you'd need to overstock so the blackhole was still safely massive at the destination which means hauling a lot of extra mass.
What David Brin calls a cavitron; in David Brin's Earth he suggests that one can possibly (we don't have the math yet) build a device that gets hold of the fabric of space and twists, and that such a device could be used to create artificial gravitational singularities that produce energy over unity in the form of Hawking Radiation. A power plant using such a device is identical to using a micro-blackhole except you don't have to take the blackhole(s) with you for the trip, you can make one when you need it and jettison it when it gets too light and hot.
A matter of risk
To clarify, energy is not renewable, when..
you own a fixed stock of fuels, after using it up you can't replace it
you mine something that is rare, e.g. fossil fuels, or methane, lithium, uranium
your mining depends on traveling (=using energy), e.g. hydrogen, deuterium
replacing the energy harvester costs more energy than the total energy it yields
your energy is converted from energy that is not renewable
You want your spaceship to have energy for thousands of years. When you want to use non-renewable energy only, choose one of the above, or some combination you trust, but keep in mind you will always run a risk of being out of fuel.. at some point in time ! The science of modern logistics provides calculations,
..to cover some max acceptable risk, by keeping sufficient stock. In space, I'd keep some renewable backup power at hand... just in case !
What about solar energy? There exist various theoretical means of exploiting the energy of a star. For example, I've read about solar sails which could be "hit" by massive mirrors funnelling a star's light towards the sail, propelling a vessel. With sufficient size or various mirror-like stations along the way, it could potentially provide acceleration for the trip.