Lets put some hard numbers on it.
MMM has already done most of the math for us.
Lets say 6 mile commute. Average sized human, going about 12mph, for 30 min is about 250 calories.
Cycling - Calories Burned Bike Riding
500 calories (in the form of food made from home) should cost about 38 cents
Killing your $1000 Grocery Bill | Mr. Money Mustache
Driving a reasonably efficient car, considering only per mile costs, is about 17 cents per mile
The True Cost of Commuting | Mr. Money Mustache
Which is just over a dollar for the 6 miles.
So, that makes biking over 60% cheaper, even if you don't factor in the exercise (no, it doesn't take the place of strength training, but it does take the place of aerobic), or the fixed costs of buying and insuring a car.
So, yeah, actually, I admit that's a much smaller gap than I imagined. But its still cheaper, and the health benefits and the possibility of going totally carless (or, of having only one car in a household with 2 drivers, instead of a car for each) push it over the top into being very worthwhile looking into it as a good way to get around.