This item is just bad.  It doesn't work if your unconcious, regens 1-6 hp per 60 rounds, at best does 1 hp every 10 rounds.  If your in a fight it does nothing, if you're out of a fight... drink a 25hp potion and regen 4-10hp in one round or take a nap, and both don't cost 20-50,000gp and use an attunement.

Quote from Mortisfilia >>

It doesn't work if you're unconscious, regens 1-6 hp per 60 rounds, at best does 1 hp every 10 rounds.  If you're in a fight it does nothing, if you're out of a fight... drink a 25gp potion and regain 4-10hp in one round, or take a nap, and neither of those options cost 20-50,000gp and use an attunement slot.

Let's "well actually" each of these very reasonable ... issues ... before addressing the main issue:

Being at 0 hp usually renders a character unconscious, but this ring still works if you are unconscious due to other considerations (e.g. asleep).

10 minutes is 100 rounds not 60, and no, the ring will never achieve a "best" rate of 1 hp every 10 rounds.  6 hp per 10 minutes is not the same thing as 1 hp per 1.67 minutes.  It never gets any faster than 10 minutes. 

I agree that the chances of the ring activating during combat are so small as to never be worth begging the DM.  On the other hand, if the ring has gone more than 10 minutes without activating because the wearer is already at full health, then it would be very reasonable to have it activate the next time they take damage.  It's really not a combat-oriented item, that much is clear.

Potion of healing cost 50gp, not 25.  But yes, a huge steady supply of healing potions would be a more inexpensive choice -- if and only if you are capable of selling the ring of regeneration, and acquiring instead a huge steady supply of green healing potions, which is by no means guaranteed.  (Also subtracting the paltry cost of a bag of holding for all those potions.)  A lot of 5e campaigns are written so that magic items are very scarce, and the price you receive for selling loot is ... not fixed.

An attunement slot is probably a more scarce resource for most characters than the alternatives.  (Alternative 1 - Hit Die heals during short rests [or potentially from the "healing surge" variant rule]; Alternative 2 - a huge supply of healing potions and the inventory logistical issues that creates; Alternative 3 - ???)  On the other hand, there may be times when a character hasn't yet filled all their attunement slots, and they may as well put on the ring until they get back to town to sell that crap.  An extra 6d6 hp during a short rest is nothing to sneeze at.

The main issue, of course, is that in addition to listing all the obvious and boring ways this item is bad, we shall also creatively think of situations in which it would be good.  Use your powerful role-playing imagination!  (That part is left as an exercise for the reader.)

Since selling some crap that nobody in the party wants is already the default action, it's not too much of a stretch to say that probably most players need to be prodded to keep, and make interesting use of, their fancy new bizarre niche magic items.  The Ring of Regeneration is no trap item, it's just niche.  You shall feel fine about selling it to a vendor; but you'll feel a lot better if you come up with a cool way to use it.

Happy adventuring!

Quote from 1Daedalus >>

What happens if the hand with the ring is chopped off?

 In old editions you could wear it on your toe and come back even if chopped up. I had a character lose a foot and escape. Later I discovered a second me had regenerated from the foot and was very unhappy that I stole his life.

This was an item I honestly hoped would see changes going into 2024, alas... it still only impacts a player's shortrests and nothing else.

Maybe its me, but this is very underwhelming to me.  It seems its more of a plot device than an useful item.  I would replace this with a ring of protection in a heart beat and thats Rare compared to Very Rare.

a buff you can homebrew onto the ring is that it removes 1 level of exhaustion during a short rest could also bump the healing to 1d8

Very Lame,
this is a common item at best

Quote from UnkKnellnapper >>

a buff you can homebrew onto the ring is that it removes 1 level of exhaustion during a short rest could also bump the healing to 1d8

A better buff is just giving the player the benefits of the Regeneration spell, or at least, closer to those benefits.

Let players regrow their limbs in 2 minutes, heal 1 Hit Point a round, and be a discount-Wolverine, lol.

The biggest issue with this item is how inconsequential it is to a player outside of a Short-Rest.