Fans noticed that the ring disappeared after last being seen in 5.07 The Curious Case of Dean Winchester. There was much speculation as to possible meanings of this, however Jensen provided the mundane explanation at Salute to Supernatural L.A. 2010:
What happened to Dean's ring?
There was an opportunity at the beginning of the season to kind of lose the jewelry. He lost his watch, he lost his uuhh... his necklace obviously went to Cas. Here's the thing with the ring, the ring was a really, for me, it was Dean's beer bottle opener. Whenever Dean opened a bottle it would just scrape off the ring, it got beat up. He also cut himself apparently. So once they were losing the watch and I was like, you know what, let's get rid of the ring. This is the Apocalypse. So I just lost it, it was like let's get rid of this we've had it on for 5 years.
In 5.16 Dark Side of the Moon there is a moment when Mary has her hand on Dean's face. A ring is seen on her finger. Some fans have suggested that it looks similar to and/or is the ring Dean wears (i.e. that he is wearing her ring), but upon further inspection, one can see it is a gold band with a diamond which is tilted to the side on her finger.
In 12.01 Keep Calm and Carry On as Mary reaches out for Dean in the opening scene, we see an even better view of Mary's ring, which is the same gold band and a diamond seen in 5.16 Dark Side of the Moon.