I wash man hands regularly, just like I've seen Meredith do on Grey's Anatomy. However- I don't think I've taken my wedding ring off this whole time.
Here's some great info published in Rolling Stone.
According to the CDC, studies have shown that the skin underneath rings contains more germs than the skin on fingers without rings.
Unfortunately, it’s not as simple as using soap and water. While a light scrub with a toothbrush and a few drops of dish soap in water can work on some pieces, depending on the material of your jewelry, you may need to invest in a UV sanitizer -- which is a great option for your phone as well -- or you can use disposable jewelry wipes or simple alcohol prep pads. (Rolling Stone)