Mine is two bottles of Potassium Iodine, in case of nuclear weapon attack/reactor meltdown.
Anyone else?
furlined leather collar and manacles.
My last two real vacations were to Hedonism2. My luggage contained about 2oz of fishnet body stocking, an inflatable raft, sunscreen and some adult toys. 
I like the way you people think.
Mine is a DVD copy of Trains, Planes and Automobiles for when my travel plans go upside down.
A plastic Slinky. No real reason. Like all good traditions, it’s founded in nonsense. There also used to be a long deflated and slowly melting purple rubber balloon, but it eventually disintegrated. The Slinky lives on.
For short trips to places near enough to not involve a plane, but far enough to warrant a hotel, I also bring scissors, a roll of tape, a plastic grocery bag, and a flashlight. Invaluable tools and material for any hotel mishap. Because you don’t want to involve maintenance in your problems. Maintenance always turns out to be an ancient, white-haired woman whose last clear memory of hearing anything was during WWII and is a little too blind to be receptive to pantomime.
A couple books. Given most people’s (non-)reading habits, this surely qualifies as strange.
Yeah, I always have my Swiss army knife, the kind with a zillion little tools. It’s come in handy countless times.
I also have a little folding toothbrush and travel sized toothpaste tube in a case, goes everywhere. The toothbrush dates back to…1996, I think, and was handed out on a Turkish Airlines flight.
What aruvqan said. 
A half-dozen garbage bags- they work great for dirty-clothes bags, waterproofing, makeshift ponchos, things to sit on, etc.