The Russians had an atomic plane, but details are very sketchy. The GE nuclear jet engines were ground tested and they would have worked, but they never flew. The possibilities of catastrophic failure were too high, and the inevitability of a crash made cancellation also inevitable.
In the end, the concept died a well-deserved death.
But here's where it is now becoming interesting. Modern technology may make this a viable concept once more. Here's how I think it just might work...
Aircraft in the 1950's were designed to be fast, faster, ever more speedy, and this means HUGE thrust and power requirements. They required people on board, meaning shielding was necessary, and shielding (and life support) is heavy. But today, the emphasis is on unmanned aircraft, with stealth characteristics, and high-lift wings with low drag. It is possible to make an aircraft that looks like a glider that can cruise with just one or two horsepower.
What we might see is an unmanned aircraft that uses electric motors and propellers to cruise, and internally is a very simple nuclear battery type of powerplant. Such a system would sustain flight at 60,000 or 70,000 feet for weeks at a time, gathering data, observing, or delivering weapons if needed. It'd still have the same issues if it crashes, but the dangers would be much less than the insane high-powered nuclear jet engines. I think it's very possible.