It is implied in Smash's thread, but I'll state it explicitly... Helicopter are so weak on defense, particularly because land units can attack them and fighters get the 2X attack bonus. Helos are dead meat in a modern battlefield.
That said, there are three times when helos might be more than expensive useless weapons.
1. Sub patrols in an AI naval game. A helo can accompany a transport, or naval task force and spot/attack subs, plus keep a 2X eye out for enemy ships. But remember, subs can easily "sink" helicopters, though!! LOL...
2. Collecting Intel/Capturing cities. If a city is beyond the range of your paratroopers, like inland a few tiles from your task force, you can use the helo to fly in and capture a city after your fighters/bombers/missiles clear the AI city.
3. Helos can suppress partisan creation. When capturing a big enemy city, and you are preventing partisans, helos can easily block terrain... particularly difficult unroaded terrain and/or terrain that can't be reached (e.g., across a narrow channel).
The clincher for me in not using Helos is a combination of their single attack per turn, slow movement (only 6), high cost, constant deterioriation, and.... drumroll... the unhappiness they cause in a Democracy. Since they can't be transported by rail for some silly reason, moving them to another city to balance things is difficult.
So for me, I don't like choppers, and rarely build them. The only unit I build less is bombers, which is almost never. Except for stealth bombers (which is of course never).