Believe it or not, this was seriously considered during the Cold War. Some manned prototypes even flew with their reactors going (albeit not to power the plane), though the problem of shielding wasn't adequately solved before progress in ICBMs made nuclear-powered bombers pointless.

Then there's Project Pluto, though that would have been less a conventional aircraft and more a terrifying drone bomber built around an unshielded nuclear ramjet the size of a bus:

The engine also acted as a secondary weapon for the missile: direct neutron radiation from the virtually unshielded reactor would sicken, injure, and/or kill living things beneath the flight path; the stream of fallout left in its wake would poison enemy territory; and its strategically selected crash site would receive intense radioactive contamination. In addition, the sonic waves given off by its passage would damage ground installations.