Hi Doug,
I'm going to suggest that the two STEREO spacecraft win this contest,if you mean traveled the farthest from Earth. Both are still in orbit about the Sun at about the same distance from the Sun as Earth is...1 Astronomical Unit..but both are separated from Earth by about 120 degrees. And this angle is increasing. When they get directly behind the Sun --directly across Earth's orbit from us -- they will be 2 AU from Earth!
The spacecraft that go to the outer solar system...Jupiter and beyond...all use a form of nuclear energy.
Paulett