I have recently started riding 3 times per week to work, I plan on increasing that to 5 days per week as my stamina builds. Based on my calculations, I estimate that we are saving (as the title suggests) $184.80/month when using the IRS Standard Mileage rate ($0.56/mile or $0.35/km).
My Bike commute is 18 km (~11 miles) each way, whereas my car commute is is 22 km (~13.6 miles) each way (due to trails).
In just gas alone, I estimate we are saving $68.57/month. This is based on my 2008 Mazda 5 getting 10.22 L/100 km (23 MPG), according to the EPA, and the average gas price in my Province of Ontario in 2013 being $1.27/litre ($4.40/Gal in USD).
So according to MMM's 10 year savings calculation - I will have saved $11,862.61 in gas, or $31,971.40 in car expenses! Assuming, of course I can keep this up 3 times a week for 10 years, or don't retire before 10 years is up!