Do I ride to save money? No. Do I save money by riding? Yes.

In addition to the original purchase price, I do spend quite a bit on cycling every year. Rain gear, winter gear, helmets, lights, tires, drive train, brake pads...no item needs annual replacement, but they all need to be replaced from time to time. Let's say $500/year, which is pretty generous. I think I spent that much this year only because I destroyed a crank and had to replace the whole crank/bottom bracket assembly.
(edit: I should mention the $500 figure actually maintains 4 bikes: 2 for me and 2 for my wife. Mine see more riding so make up the larger share of the cost, as well as a larger share of the benefits)

But a car...if my family needed a second car because I didn't bike, that's like 30 years of cycling expenses up front...for a cheap car. Even if we just burned an extra tank of gas every month, that would equal or exceed my cycling costs. Buy a bus pass to replace the bike commute? Roughly equal to the cost of biking (and only because there's a tax credit and my company kicks in 1/4 of the cost). Pay for parking to replace the bike commute? About 4x the cost of biking, ignoring the vehicle operating costs.

And then there's other things. My life insurance medical puts me in the healthiest category (despite being overweight). I thank cycling. Annual savings of around $100. Extra life expectancy priceless. Cycling's door-to-door convenience (I park inside my office and inside my home) means it's actually faster than driving for me, and also faster than the bus. If we assign value to the time (I generally don't, since I have no practical way of earning more money by cutting the commute time), it's probably worth around $15/week or $720 over the course of a year (48 work weeks).