I think bicycle commuting is quite a bit cheaper for those who can go without (or reduce the number of) car ownership. For my wife and I, we need a second vehicle often enough that I keep it around which means I'm still paying maintenance and insurance, plus I had to buy the thing initially. Riding my bike to work reduces the amount of maintenance I do and gas for this vehicle, but it's still an expense. So for me the answer is "yes it is cheaper but not by as much as one would think."

When I first started commuting we owned three vehicles plus a motorcycle. I was able to give up one of the cars (against my wife's protests) so by eliminating that entire vehicle from our stable I saw a reduction of expenses at that time.