This is a very common question and something that I honestly learned the hard way about a year ago.
Shortly after my wife and I got married, we took a short honeymoon to South Carolina. As I was passing through the airport security, I had taken off my wedding ring and placed it in the plastic bin with my shoes and jacket. As my wife and I were walking to the gate, she made a comment about our rings, and as I looked down, I was in complete shock as I noticed I left my ring at the security checkpoint.
I ran back to the supervisors desk and asked if someone had turned in a white gold ring. After some joking and teasing, he handed my ring back to me, and told me that it was not necessary to remove rings, earrings, or necklaces unless requested.
While I was relieved, I learned a valuable lesson that day. While the Transportation Security Administration (TSA) may be crazy and adamant about taking off your shoes and belt, and making sure your laptop is in its own plastic bin, they at least give us the benefit of the doubt by allowing us travelers to wear our jewelry.