Over the course of its existence, Lord of the Rings' One Ring had a number of Ringbearers. After Sauron lost it in the Battle of Dagorlad, the Ring was briefly owned by Isildur before Deagol found it in the Anduin River. Wanting it for his own, Smeagol savagely murdered Deagol and kept the One Ring for over five hundred years. Then, out of nowhere, Bilbo Baggins showed up in the Goblin tunnels and "won" it in a game of riddles.
After that, Bilbo kept the ring for a few decades before passing it off to Frodo in an incredible show of Hobbit strength. Frodo would eventually take the Ring to Mount Doom and destroy it, but at first, he didn't want to. He desperately tried to give the Ring to Gandalf. Luckily, the Grey Wizard refused, and it's a good thing he did. If Gandalf had taken the One Ring, he would have become a worse Dark Lord than Sauron.
Gandalf Could Have Defeated Sauron With the One Ring
LOTR fans know that Gandalf was more than a wandering wizard. He was really an angelic Maia, named Olórin. He was actually one of the wisest Maia in existence, and that was why he was sent to Middle-earth in the first place. He, along with Saruman and Radagast, arrived mid-way through the Third Age to exhort the free peoples against the dormant evils of Sauron. He -- unlike his Istari companions -- was committed to his task and was even willing to sacrifice himself so that the Fellowship could continue its quest.
Between Gandalf's Maiaric power and his legendary wisdom, one might think that he could have put Sauron's Ring to good use. That would have been true to a point. If he had taken the Ring from Frodo in Bag End, he could have combined his natural strength with the power of the One Ring. That probably would have been enough to overthrow Sauron. However, that would have been awful for everyone.
Evil Gandalf Would Have Eliminated Everyone
Sauron was bad, but as this Quora thread explains, Gandalf's perception of good and evil would have made him a terrible Dark Lord. In his wisdom, he would have used the One Ring to set things right, but eventually that wouldn’t have been good enough. The longer he ruled, the less anything would have measured up to his standards. Soon, he would have started eradicating the things and the people who weren't good enough for him, and that would have continued until nothing was good enough. Eventually, evil Gandalf would have eliminated everything and ruled in solitude.
Gandalf might have been able to defeat Sauron, but that would have only made things worse. Gandalf knew that, which is why he refused to take the Ring in the first place. That makes sense because The Lord of the Rings champions those who refuse power. Boromir died peacefully after he repented for trying to steal the Ring. Likewise, Galadriel passed her test when she refused the Ring. In declining the One Ring, Gandalf showed his incredible wisdom. He knew that the One Ring would have corrupted anyone -- including himself. Thus, he allowed Frodo (who didn't have the power to challenge Sauron with it) to destroy the Ring in Mount Doom.