As mentioned, they are already used on geosynchronous satellites (made by http://www.boeing.com/defense-space/space/bss/factsheets/xips/xips.html , among others). These thrusters are very efficient (the ions are expelled at around 30,000 meters/sec), but can't throw out many particles per second (about a quarter of a milligram per second). The result is very weak (around 80 mN - the 165 mN spec is max, but normal operation is about 80 mN), but very efficient thrusters.
Of course, even weak thrusters will give you some acceleration and a very long acceleration will eventually get you a high velocity. But you'd really want more powerful thrusters if you wanted to accelerate a large spaceship reasonably quickly.
And a reliable source of electrical power. The particles are electromagnetically accelerated and the engines take a huge amount of electrical power (around 4500 Watts for 80 mN thrusters). With weak thrusters, large solar arrays, and being relatively close to the Sun, that's doable. (I'm not certain, but I think the reliability problems mentioned by etudiant had to do with strategies used to get more solar power per unit of area in order to keep the solar arrays from getting too big. I think the variations with the large, but traditional solar arrays are pretty reliable.)
For an interplanetary mission to somewhere like Pluto (or beyond), with an engine that's going to take humongous amounts of electrical power, you're going to need some other fuel-fed power source to supply electrical power to the engines, which somewhat negates the fuel efficiency achieved by accelerating the particles to such a high velocity.
There's no magic bullets. It takes energy to move a spaceship. If the energy is coming from somewhere else (the Sun), you're lucky in that you don't have to carry your fuel source around with you. If you have to supply the fuel for the energy you need, you wind up carrying around a lot of fuel no matter what method you use.
But nuclear energy at least provides a lot of energy for the amount of mass you're carrying around.