Okay, so I was over scanning the news at EN World as I do occasionally and saw an announcement for a board game where you play the Nazgul in The Lord of the Rings. I immediately thought that would be a cool basis for a campaign where the PCs are evil. The usual problem with campaigns where the characters are evil (or mixed evil and neutral) is that they soon fall apart as the party members backstab one another (often literally backstabbing). So making them bound servitors of a powerful evil entity would force the party to restrain its self-destructive impulses--well until maybe they were powerful enough to challenge the evil entity and take its place. I believe the evil adventure path Way of the Wicked from Fire Mountain Games involves the PCs signing infernal contracts to get broken out of prison, but naturally there's a price.
Of course being bound could take various forms, not necessarily matching magic rings. A good example is the Abyssals in Exalted. The abyssal exalted are the super-minions of a set of dead/dying gods. Once mortal, they were made an offer in their dying moment. That dying moment typically was one of great dramatic emotion. If they take the offer they can become one of the immortal servants of the undead abyss.
Another approach is a variation on one I tossed out as a campaign idea earlier, where all the characters (in a D&D/Pathfinder type game) voluntarily become liches to survive an apocalypse. In this variation they all become liches voluntarily in order to survive something, but the phylacteries which hold their souls are in the possession of another.
Or perhaps the evil power hold hostage someone they care about. Yes, even evil types can care about someone even while admitting to themselves that it's a weakness. Imagine the campaign opening: each of the PCs arrives home and finds one of those notes made of letters cut out of books spelling out something like "WE GOT YER KAT". A mysterious emissary arrives soon after and explains that unless the PC does exactly as they are told then little Fluffy will not be given even one single treat. No, not even one morsel. Now that would be evil. Bastards.