In short, if Sri Lanka had a national vehicle, it would be the tuk-tuk!
Tuk-tuks are my transportation of choice. While buses are convenient and cheap for longer trips, tuk-tuks simply make sense for the day-to-day. In Sri Lanka, when it rains, it pours. I'd rather spend $1.25 on a ten minute tuk-tuk ride to school than be soaked through by the time I reach the end of my road. Besides, they aren't difficult to locate. I am bombarded by "Tuk-tuk, Miss!" everywhere I go. They are the taxis of Sri Lanka, and they get me where I need to be and offer a breezy respite from the city's oppressive heat.
Truthfully, I don't know the history of tuk-tuks and Sri Lanka, but in a tropical climate, they are arguably the most attractive option. They are easy and breezy. I also believe tuk-tuks are suited to a country without a universal highway system. They aren't as fast or powerful as a car, but their gas mileage is astounding regardless of whether they are navigating a city or pothole-infested roads amidst rural villages and paddy rice fields. This mode of transportation also employs a significant fraction of Sri Lanka's (male) population, catering to natives and tourists alike.
