Was tried in the 1950s' by both America and the USSR. I believe the russians actually flew an aircraft with an experimental nuclear engine as well as conventional ones. I don't think the American effort got past the drawing board.
The main problems are the obvious ones. Radioactive exhaust, radiation shielding for the crew and passengers and flying around with an atomic reactor on board (imagine the first time one crashed!!).
Theoretically possible but with some HUGE hurdles.
Interesting article
HERE
Edited to say- read this realising the previous four replys crossed with mine!!!