As an industrial maintenance mechanic in the food industry, I must remove my wedding ring and wristwatch while at work. GMP regs, but with good reasons from both safety and sanitation standpoints.
I'm a southpaw. When I'm at the range for regular "basics" reinforcement drills with a handgun, I generally remove my wedding ring and put it in the "watch" pocket of my jeans. There are a couple of reasons for this, both at least somewhat pragmatic.
First of all, it's pretty hard on the ring. Especially if there's checkering on the frontstrap of the weapon. 18 ct. gold is much softer than steel, and before I started doing this regularly my ring got pretty chewed-on looking. It gets enough collateral damage in the course of everyday life, so I try to preserve it from whatever unnecessary indignities that I can.
Secondly, I've noticed that some marring on the grips and/or frontstraps of several of the nicer pieces that I don't generally use as "working" guns. It doesn't matter to me much on carry or field weapons, but it kinda pains me when I see it on the "Gee Whiz" stuff where condition is everything. Sole exception here is my CZ 97-B, where I'm just too cheap to want to spend the money to replace the polycoat finish until I absolutely must.
I went through a lot of watches before I swapped which wrist I wear it on. Even the best of mechanical watch movements will eventually fail when they're subjected to repeated recoil of the .45 hardball variety. Haven't had one fail since I began wearing it on the right wrist.
SD and CCW drills the ring stays on for the above-mentioned obvious reasons. If a problem is going to come up that'll affect accuracy, speed or function I want to find out about it and solve it before it has a chance to cost me or mine our future.