Since the purpose of minimum parking regulations is to create an inefficiently large quantity of parking spaces, it's no surprise to learn that minimum parking regulations create an inefficiently large quantity of parking spaces. That said, this is actually a controversial point, so I recommend to all interested in the subject this NYU Furman Center report on New York City parking regulations (PDF) which finds, among other things:
Building patterns suggest that developers would build fewer parking spaces without the requirements. Of over 300 recent housing developments in our sample that were subject to a requirement, 77 percent built at or close to the parking requirement. Small (5-9 unit) developments subject to parking requirements built an average of five spaces–exactly the average mandate. Developers of small buildings for which the requirement was waived, on the other hand, built, on average, just half of a parking space.
These parking minimums are one of the main reasons that the rent is too damn high. That happens through several channels. The first is simply that providing the parking spaces is costly, so an above-market quantity of spaces per housing unit leads to more expensive units. The second is that there are often logistical limits to how much parking it's possible to provide (garages can only get so deep, for example, before costs become prohibitive) which constrains the construction of new housing units, leading to scarcity and high prices.
An additional consideration is parking cycle lock-in. One reason that car ownership in Manhattan or Paris is relatively rare is that so few people own cars. With lots of auto-free households around, it makes sense for businesses to cater to the needs of carless families which reduces the utility of automobile ownership. Conversely, the more you subsidize car ownership by requiring the construction of more parking spaces than there's demand for, the higher the utility of automobile ownership becomes. The ultimate impact on housing prices can be ambiguous, but the impact on the environment is extremely bad.