There are practical problems with traditional wedding rings. Some people (myself included) just don't like wearing any rings because they find them uncomfortable or distracting. And The Abyss (in which the hero's wedding band saves him from crushed fingers) notwithstanding, people in certain professions (such as surgeons, electricians, or martial arts instructors) shouldn't wear rings on the job due to health or safety concerns.
Frequently-removed wedding rings can easily be lost. Losing an expensive ring is no fun whatsoever -- my mother lost her first wedding ring, a family heirloom, one day when she was surf fishing in the cold Atlantic, and forty years later she still speaks wistfully of the ring.
If you take the opposite tack, and don't ever take your wedding ring off, over time as you gain weight or your joints get bigger it can get stuck on your hand so that you can't get it off. An older friend of mine was suffering from an illness that caused his hands to swell, and his wedding ring started cutting off the circulation to his finger. He tried several home methods to get the ring off, but eventually had to go to a jeweler's to get it cut off his finger.
Some friends of mine who recently married came up with a very simple solution: they got rings tattooed on their fingers. They came up with the design themselves: the center of both tattoos is an infinity symbol. While they didn't want regular rings (he doesn't like them and she felt she was likely to lose a ring or any other jewelry) they wanted something to represent their commitment to each other. Tattoos seemed perfect for their purposes.