In addition to John's post...
With so many foreclosures happening in recent years, there's been a massive backlog and many homes that were discharged or defaulted on have not yet had the foreclosure proceedings completed. I've had three clients in the past four months already who discharged their house or defaulted and 2-3 years later, the bank still hasn't foreclosed. Unfortunately for these people, they're finding it extremely difficult to obtain financing again due to the lag time in the foreclosure process. VA doesn't care about this window, your "time" starts from the discharge date but most lenders will use a credit overlay to make it match their FHA guidelines.
Post-foreclosure for conventional financing without an extenuating circumstance is now SEVEN years. If you're debating doing a short sale or letting them foreclose, avoid the foreclosure at all costs if you don't plan on renting for seven years or going with a FHA loan after your three year window is up (three years as of when I write this, that time frame could increase in the future).
Best of luck to you.