When India was divided, there were a few princely states that didn't want to join either country they were enclaved by or wished to remain independent. These included Jammu & Kashmir, Hyderabad, the Khanate of Kalat, Travancore, Bhopal, Jodhpur, and Junagarh, as well as several territories administered by foreign powers such as the French or Portuguese. Most either accepted ascension to one nation or the other, or were annexed by force.
I can't help but wonder how strange it would be to see an Indian subcontinent with a patchwork of states.