After the collapse of the Soviet Union, Ukraine inherited a huge nuclear arsenal, which it subsequently gave up. In return it received assurances from Russia, the United States, and the United Kingdom that its territorial integrity would be respected. These assurances were embodied in the Budapest Memorandum of 1994. While the United States and the UK complied with that agreement by not invading Ukraine, Russia did not.
What if Ukraine had retained its nuclear arsenal? It seems more than likely that Russia would not have invaded Crimea. Putin might have calculated that Ukraine would not have used its nuclear weapons in defense because then Ukraine would itself have surely been obliterated by Russia. But the risk of nuclear war would have been too great; Putin would have stayed his hand. (However, it is possible that Ukraine would have been forced to give up its nuclear weapons one way or the other long before 2014.)
So between meaningless paper security assurances and nuclear weapons, the latter provides a bit more security. One implication of the Crimea crisis may be the further unraveling of the nuclear nonproliferation efforts that President Obama has made the centerpiece of his foreign policy.