If nothing else, it amuses my nieces and nephews!
On the road between Patong and Karon, there are several places offering elephant rides in the "rainforest." The advertised price for the ride was about $15 per person, with two people riding each elephant. They weren't busy and this IS Thailand, so we bargained to about $10 each for four people - each with our own elephant. A guide accompanied each of us. Your picture will be snapped at the beginning of the trip, with prints available for purchase at the end of the ride. Guides expect a tip of about 10% of the regular price.
This wasn't really my idea of a rainforest. A path was cut through a wooded area, giving you a sense of being in a forest, but you could occassionally hear noise from the road nearby. There weren't many interesting animals or plants to see. As one might expect, though, there were plenty of bugs. At a couple of points, we got a beautiful view of Karon Beach.
On the whole, this is a good way to kill an hour or two and might give you an interesting story to tell the folks back home. I wouldn't put it high on my list of things to do on Phuket though.