Does a zip line count? It's a pretty different way to travel. ;)
I've also ridden on an elephant before as part of a trek (as well as a few other times in various places) and the peak tram in Hong Kong was another great experience.
A camel ride would probably be the most unusual. Apart from that, it was a novelty for me to ride in the back of a ute while I was abroad, in a country where it was legal not to use seatbelts or seats.
Rode a camel to Dinner venue once. That was enough!
Travelled by tuk-tuk, horse carriage, horse, aircraft to a concert in another city, helicopter to stables to go riding, rubber boat on Rapids, tinnie through caves, chauffeur driven car to functions, 'Chinook' to Base Camp, & legs on many a scenic bushwalk!