According to Wikipedia, the average North American car gets 20.4 miles per gallon. Even though there are ways to get better mileage, not to mention the fact that Japanese and European cars, diesel, and alternately-fueled cars get better mileage still, nothing beats the bike.
We all know that bikes require fuel, too. It’s called food. So your fuel efficiency is going to depend on what you’re eating. According to one estimation, you can increase your fuel efficiency 529.4% relative to the average North American car by riding your bike assuming you eat SAD-ly (that’s Standard American Diet, which is aptly named given the acronym).
Here’s the cool part. You can further increase your fuel efficiency 188.5% by eating a vegetarian diet, too. And as was pointed out in the comments in the aforementioned estimate, if you eat local, you’ll increase it further. Eat right, consider appropriate transportation, save money. Everyone wins!