As a youth I decided against getting a drivers license. I did so for the following reasons but I admit that it surely contained a bit of idealism:
cost of a drivers license (in Germany this is notable; I hear 2000 EUR)
time to get the license (in Germany it's mandatory courses and driving practice)
cost of the car, gas, maintenance and replacement cost (my Budget says that for used cars is with 10000 km/yr is ~ 5000 EUR/year)
pollution and other environmental costs (this was a significant consideration for Gunnar_1987)
time driving the car (during which you could do more sensible things; this is covered enough by the other comments)
I still do not have a drivers license and don't regret it (and before you ask: The car was my ex-wifes).
The lost freedom to go anywhere I please anytime - which was and is so highly valued by my peers and parent generation didn't factor notably in my consideration. Today even less than then. The internet gets me most places - even if only virtual (but safer), even where no car goes anyway. From the saved time and cost I can afford lots of cab rides - more than I need. And I wonder where the saved time payed off with lots of interest by the additional amount of study (leisure style) it allowed.
But your mileage (pun?) may vary depending of your location.
Even if you don't plan on driving, I recommend getting a license (at least in the US). Insurance rates fall significantly if you've had a license for 7+ years, even if you've never driven.
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This post is on commuting and transportation.