The Indian equivalent of the pony ride, is, not surprisingly, the elephant ride.
This elephant, who is now 37 years old, became the giver of rides for tourists and birthday parties after having been rescued from malnourishment and the back-breaking labor of years of hauling lumber. I was lucky enough to be able to get lots of hugging from her before people gathered for their rides. She especially liked to be scratched behind her ears.
Though the ride was rather tame–or perhaps because tame (i.e. gentle)–I rather enjoyed moving with this gracious being. A horse might now seem small (though likely feistier).