All new passports issued by the US, and many other countries as well, contain RFID devices. While the government claims that this will not be readable by RFID readers other than theirs, you can bet this won't be the case for long.

In the US, a non-working RFID device does not invalidate your passport. But the act of disabling the RFID device is a crime. So, if you want to take your chances, here's a way to disable the RFID device so that it does not appear intentional... although I am certainly not recommending that you take part in this illegal activity. That said...

The RFID device is in the back cover of the passport. You can disable it by crushing it. Don't just take a hammer to it though, cause this will leave marks and it'll be pretty obvious you disabled it. Instead, get some pieces of hard wood (like oak) and lay it behind the cover and put one over the cover (you are making a sandwich: wood/cover/wood). Then beat the crap out of the wood with the hammer being careful not to leave any marks on the page itself until anything that just so happens to be in the cover will be smashed to bits.