There are at least two problems with solar photovoltaic cells (not considering concentrators) in the outer solar system: the low power of the sun, and the low temperature of the cells.
For the Cassini mission to Saturn (9–10 AU from the Sun), NASA investigated solar as an alternative. They calculated the surface area that would be required, and concluded that the mass of the solar arrays required would result in a spacecraft with a mass exceeding anything that could be launched with existing technology, and would severely inhibit manoeuvrability. They concluded that it would have been possible, but that the scientific cost would be too high:
From the Cassini Environmental Impact Statement, chapter 2, page 2-53 onward. For one alternative configuration,
The addition of this size array, in conjunction with the other modifications required to implement solar power, increased the spacecraft dry mass by 1,337 kg (2,948 lb). With the mass of the propellants, the Huygens Probe, and the launch adapter, the total spacecraft mass would increase to 7,228 kg (15,935 lb), far exceeding the launch capacity of the Titan IV (SRMU)/Centaur of 6,234 kg (13,743 lb) for a trajectory to Saturn (JPL 1994a).
or, for another one,
To further reduce the size of the arrays, the power available to the science instruments was reduced by 50 percent. Because of the large moment of inertia created 2 by the large solar panels (397 m²[4,269 ft²] and 585 kg [ 1,290 lb]) (JPL 1994a), the time required to turn and maneuver the spacecraft during its exploration of the Saturnian system would increase by a factor of between 4 and 18 compared with the compact RTG-powered spacecraft. The resulting impacts on the mission's science objectives would be serious and include increased times for image mosaics, inadequate turn rates for fields and particles instruments, reduced image resolution due to inadequate target motion compensation, loss of instrument observation time during turns for communicating with Earth, and insufficient turn rates to support radar observation of Titan's cloud-enshrouded surface.
More recently, two missions to Jupiter (4.9–5.5 AU from the Sun) use solar arrays: NASA's Juno is currently (2013) cruising to Jupiter, due to arrive August 2016. ESA's Juice is to launch in 2022. Both use solar photovoltaics, and are the furthest-away spacecraft to do so to date.