Well, a lot of it originated around street parking. When cars were becoming very popular and common, they would generally be parked on the street. Of course, since most street parking spaces were not metered (that is, free parking) this meant that parking was constantly scarce. Huge parking congestion, conflict over spaces, etcetera. Even where the parking was metered, the price was usually set too low (since it was owned by municipalities, with no incentive to maximize revenue). So street parking was still congested everywhere, but the straightforward solution of just raising the price of street parking was too unpopular for most cities.
This led, mostly post-1940s, to urban planners requiring homes, businesses and offices to have a minimum amount of parking. However, the way they usually determined the "appropriate minimum" was to estimate the maximum probable use: measuring the busiest day of the year at a shopping mall, or requiring one parking space per bedroom in a house, etcetera. This basically ensured that, no matter where you go, there's almost always parking available. However, this also means that most parking is never used. The secondary effect of this means that everything becomes surrounded by large amounts of parking, causing everything to be further apart, making driving much more appealing. Also, people become very accustomed to free parking, so anywhere that there is a parking shortage, they demand not better pricing, but more mandatory supply. In the US at least, you will typically only pay for parking in areas built before 1940.
But it's not necessarily US-centric. While the US tends to have the most extreme parking minimums, they're common all over the world, from England to Malaysia.