Unfortunately the Federal Government doesn't issue a 'Veteran ID Card'. The Department of Defense only issues cards to Active Duty, current Reservists, Retired personnel and their dependents. The Department of Veterans Affairs only issues cards to Veterans who are currently enrolled and using VA health care.
Department of Defense Common Access Card
If you're eligible for a DoD card I probably don't have to tell you how to get replacements or cards for your dependents. I'll just give you the link.
Department of Veteran Affairs ID
The only way you can get a VA card is to enroll for health care from the VA. You can enroll by submitting an annual application and occasionally having a short physical. Many people who maintain their VA eligibility still use their regular insurance or Medicare (and doctor) for their routine healthcare.
If you're eligible, having the VA hospital system in your back pocket isn't a bad idea in itself. Most prescriptions are much cheaper and the co-pays are much lower than Medicare or other insurance programs. It also counts as a health care program under the new Affordable Care Act that goes into effect in 2014.
We cover what you'll need to know to enroll on our Veteran's Health Care page. If you have more questions you can reach us at 888 777-4443 Monday through Friday, from 9:00 AM until 5:00 PM Pacific time.
State Verified Veteran Status
Many of the various State governments have stepped in and provided a logo on their Driver's and ID cards that will verify your veteran status. The logo won't be accepted as legal proof of eligibility for Veteran's benefits, but just about any business that offers discounts will honor it. The most up to date list that we're aware of can be found on militaryandveteransdiscounts.com.
If you're aware of a newer list, let us know and we'll update.