Nukes can cut 50+ unit stacks to pieces in no time flat. The diplo penalty is a bit unbearable though...but good for taking down a last superpower if it comes to that. There are other options but nukes are pretty effective.
A more common use for nukes is when you're gunning for space and there is a big rival on another continent. If that guy declares on a weaker AI that would vassal, don't allow it. GIFT nukes to that weak AI right next to the big one's stack, and watch the fireworks. The best part is that you get no negative diplo for gifting nukes at all. A pair or trio of tac nukes should maul even the greatest shaka stacks. There goes his power, and any hope for war success!