I've twice been stuck in elevators. Both times in India. Both caused by power cuts.
The first occasion, in a modern well-equipped hotel, http://www.hotelsfo.in in a brand-new new lift was weird, rather than scary. I was on my own. The emergency lighting came on, then the emergency power and the lift returned to the 19th floor, according to the display. Unfortunately, I knew the hotel had only 4 floors! It then made its way to the basement, almost - it actually stopped about a foot too high. But I got out anyway, and used the stairs. The lift obviously re-booted itself later, and was working fine an hour later.
The second occasion was at my office in BTM layout, Bangalore. http://www.novelteam.com/index.php/novel-office-space/locations/novel-business-center
On this occasion, no light, no power backup. The lift "failed safe" (i.e. We were stuck and not moving). There were about half a dozen of us in there, in 90 degree heat. We kept a certain amount of light in the place using mobile 'phones. No-one panicked, not even me (and I hate confined spaces). About 20 minutes later, the power returned, and we were able to complete our 50ft journey.
I still like India :)