Holy lamp oil! This thing could eat a campaign!
To understand what I mean, let's start with the item itself.
"The wearer may summon one djinni to serve for up to one day. The djinni will only serve and obey the person wearing the ring when it is summoned, even if the ring is then given to another character. (See MONSTERS for a description of a djinni.) The ring may only be used once per day."
So one use per day, only one person (the wearer) gets to command the djinni. OK, seems pretty straightforward. Here's the thing about that: a djinni can be summoned each day and can hang around for up to one day! That means the owner of the ring effectively has a djinni on continuous call. Sure, it might get killed and then he's out of luck until tomorrow, but let's talk about the djinni itself.
Move: 90' Fly: 240'
Att: 1 + special
Dmg: 2-16 (fists), or 2-12 whirlwind
So it's got several very cool powers apart from combat. It can create food & drink, it can create metallic objects (temporary) and soft goods (permanent!), it has invisibility, gaseous form, illusions, and whirlwind. It can do any of these 3 times/day. They can also carry fairly heavy loads without tiring.
Having one of these on call would drastically shift most combats in the PCs' favor. Admittedly less so at higher levels, but if the ring were randomly rolled who knows when it shows up?
Three noncombat things jump out at me about the djinni though: 1) the object creation powers and 2) the flight speed and 3) the load carrying.
Why these three? Because if I had a PC with this ring, I would become insanely rich in a very short amount of time. I would have the djinni start by creating beautiful gold statues, as well as things like tapestries and carved wood. Then –while disguised by its illusions and it invisibly watching over me– I would sell the stuff for thousands of GP (preferably in gems). I would then have it fly me the HECK out of town before the gold disappears the next day. Once in a new town, I would repeat the process.
Cue the getaway music!
Now, as a card-carrying member of the SOB GM club, I could definitely find ways to screw with the party that tried something like this. More likely, I would let them get away with it for a bit, then catch them out. Either that, or maybe an NPC might be running the scam and the PCs get blamed.