It looks as though I'm the only one here who voted for paratroopers, which is surprising. Skillful use of paratroopers will give you the upper hand in late-game wars.
Moff Jerjerrod's post, above, had the idea exactly right. If you've got an annoying neighbor who's about to declare war on you, you can use paratroopers to make his life hell.
Your plan should go something like this. First, build a bunch of paratroopers and station them in all your border cities. When the enemy declares war, drop them onto every strategic resource within range. Pillage and fortify. If you can't reach any strategic resources, use them to take out gold mines, or mined hills and mountains near enemy cities. (This is also why I like to fortify troops over my own strategic resources. Don't want to give the enemy any ideas.)
Result: the enemy takes a hit in production, and they have all these paratroops behind the lines. Firepower that would be going to strike at your homeland is instead being used to take out a lot of strongpoints in their own territory. This should give you time to roll in the invasion force.
You should expect paratroopers to have a high casualty rate, but if you use them wisely, you'll get quite a lot of bang for the buck out of them.