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. We then realize that the ring is Mary's ring. John also has a similar ring in some episodes, making it seem that they are their wedding rings.