I was towing canoe trailers for a summer job once. Nothing too heavy, but with 10-12 canoes on each trailer. I had a co-driver with me who never towed before. I towed out the first couple, taught him how to hook it all up - proper use of chains, coupler, wiring etc. On the third trailer, I got a few Km's out, hit a bump and the trailer was bouncing around. Luckily the chains caught the trailer and there was little damage. The only damage was that half of the plastic crank handle was ground off. Luckily, the tongue of the trailer slid under the truck and made contact with the hitch, so the truck was uninjured.
So what happened? There was 7 of these trailer and they were identical, same make/model/size. However, ONE of them had a larger coupler then the rest. It just so happened that it was the one he hooked up. He did everything correctly except lift the tongue to make sure its connected securely (these trailers are light enough to do so). The blame was really mine, however, as I did not check the connection beyond a visual check (I also didn't lift the tongue).
Like I said, luckily no one/equipment was injured. I definitely learned my lesson and check the coupler size now. The scary part is how far I was able to go before there was an issue, those chains definitely saved the day. I always used the chains and thought of it as a redundancy until then. I wouldn't even consider to tow a trailer (on road) without them now.
For those of you who haven't experienced it, its bouncy and shakey, but the trailer was otherwise stable (not swaying). It felt more like trailer brakes coming on and off. I very slowly came to a stop, making sure the truck was pulling the trailer as much a possible, to avoid truck/trailer collision. However, the tongue still did hit the hitch and had it've been offset left/right there would have been damage to the bumper, tailgate and canoes (possible something could have gotten snagged underneath, too, I guess).
^^Moral of these words: use your damned chains, and use them properly.