That's a daunting task, but I can get the ball rolling. Others may chime in to help with all the stuff I inevitably leave out or get wrong.
Nukes leave fallout (amount determined by rng and difficulty level) in some of the tiles immediately adjacent to ground zero. Fallout has additional effects depending on your game version and if you use a MOD (global warming, nuclear winter, unhealthy penalties, etc).
Nukes provide hitpoints against all units in the same radius (including your own). This can kill or leave them damaged but alive.
Nukes destroy tile improvements in the blast radius.
Nukes give you negative diplomatic points (-1 "You nuked our friend" from every civ not annoyed or worse with your target) and (-2 "You nuked us" from any civ you nuke). These diplo modifiers are permanent (never fade, never forgotten) and cumulative (add up for each and every nuke you launch), and max out at about -100 (they'll really hate you by then

).
Nukes (having them, not using them) increase significantly your power rating, providing a quite effective deterrent, (they won't likely declare war on you even though they hate you if you are way more powerful than them) -- this is particularly true for non-nuclear civs. But if their power is close to yours, it won't deter anything, and will more likely trigger a massive retaliatory strike if you use them (and your power drops as they are expended!).
Nukes allow you to see parts of the map that you would otherwise be blind to (the 9 tile detonation zone), and thus can be used like Madscientist in one RPG to locate that last remaining 1-pop city that you need to get for a conquest win.
Anything else?