It also gives you unnaturally long life. Gollum lived over 500 years with the ring. Bilbo had the ring for 60 and didn't age a day until he parted from the ring and took a nose dive
It also controls all other rings of power and the people wearing them. If powerful people wear the minor rings, then the wearer of the one ring would effectively control that power too.
But for the porpuse of this thread, it looks like there is no other rings to control, so you just get invisibility and nigh immortality.