The ESA is developing Radioisotope thermoelectric generator based on Americium 241. It's got a half-life of 432 years so it could power a probe that lasts for centuries.
It's not just the power supply though, also the thrusters for maneuvers. As an example, Cassini is nearing the end of its lifetime, and that's mainly because it's run out of fuel for maneuvers.
There, use of ion thrusters as for the Dawn mission to Ceres could help as they use very little fuel. And use gyroscopes for orientation to point towards Earth.
If you mean also - how far away can it go and still keep in touch - well there it could use thin film mirrors to create a large telescope to use to communicate back to Earth. Or a fleet of smaller nanoprobes working together. There are ideas for ways that probes could communicate back to us from another star by that method.
Project Icarus (interstellar) is a project to design a probe that can get to another star within a century and communicate back to Earth. So the engineers involved in that project think it's feasible to build a probe that will last for a century and communicate with us from several light years away. We couldn't do that right now with off the shelf technology, nowhere near. But they think it is something we could do potentially in the future.
ADVANTAGES OF AMERICIUM 241 FOR LONG DURATION MISSIONS
Plutonium 238 is what is usually used. This is nothing to do with the Plutonium 235 used for nuclear weapons. Often isotopes of elements have very different properties. Instead Plutonium 238 is so radioactive it is actually hot. And doesn't enter into chain reactions like Plutonium 235. It has no value for nuclear weapons at all.
It has a higher power density than Americium 241, so for short duration missions, you need four times as much or the Americium 241, because it produces 0.1 watts per gram compared to 0.4 watts per gram. Though it does this with five times the half life (approx).
Still for many centuries long missions, Americium 241 is better than Plutonium 238 with its half-life of 87.1 years.
If you had the same mass of Plutonium 238, you'd have four times as much power initially, but after 87.1 years it is down to double the original power of the Am-241, after 174.2 years it is down to the same as the original power of the Am241, and after 261.3 years it is down to half the original power output of the Am 241. By the time the Americium 241 is down to half of its initial power, the Plutonium 238 has gone through five half-lives so is now down to an eighth of the initial power output of the Am241.
Or to put it another way if you did want something that lasts for 432 years with a particular design power level at the end of that time period, you'd need four times as much of the plutonium 238 to achieve this as the Americium 241.
If you only need it to last a century or two, you need less of the Plutonium 238.
The situation is also improved because Americium 241 is purer than the Plutonium 238, isotope purity 99%. The ESA would be better off using Plutonium 238 but I think it is political reasons + availablity - that they have plenty of Americium from processing plutonium. And it has the side effect that their missions will last much longer with little reduction in the power levels.
Anyway in this context, then if you want to last as long as possible, and you use RTGs then Americium is the way to go.
You could also look into other approaches. But an Amerecium based RTG would seem to do just fine so we have one solution already.