The nuclear weapon is prominent in our culture. For 7 decades, nuclear power has stood as the ultimate destructive force we can unleash.
The destruction of Hiroshima and Nagasaki left an impression on the lives of a generation, effecting everyone in the world in a way that even the moon landings didn't. A single weapon, possibly launched by a single man, brings destruction that can only be described as biblical in scope.
The device also emits radiation, which has been very poorly understood by the common layperson for over half of those 7 decades. So the god-device we used is also magical.
Humans also tend to think in terms of plateaus. In general, we don't talk about something wiping out a 10-foot circle. We say a grenade can kill a room, a bomb can kill a house, or a building, or a city block. Bigger bombs can kill a city, or a county, or a state. We don't understand scale, we understand metrics. The bombs dropped to end WWII killed cities, wiped them from the face of the earth.
Until a device which can kill a county or a state is actually used, the human psyche will continue to think of the nuke as the biggest, baddest, most terrifying weapon imaginable.
Therefore, it's understandable that it is used to wipe out powerful foes (Like the Stargate movie) or strike back at nature (Armageddon). It's also understandable that we would seek to use it in constructive manners (Sunshine, The Core) - after all, anyone can DESTROY. As has been the case since man first tamed fire, it's not until you can turn a destructive force towards constructive ends that you truly master it.
In short, SF uses nukes to destroy our enemies, and speaks to our desire to master the monster we unleashed so that we, as a people, can move on.