In my experience, the best 'cursed' items are so subtle as to make uncursing them seem confusing. I've seen someone who stole from a temple's reflection pool, cursed to never get a good deal at market again, and regularly got 50-90% of the gold he SHOULD have gotten. It started immediately after the incident, and he had a hard time placing what was happening, and an even harder time figuring out how to break the curse.
If you're dealing with a ring that was held precious by BBEG, then it stands to reason that it's an artifact of power, important to his continued reign. This could be played much in the way of Lord of the Rings, as it bestows surprising power, but also takes a drain on the user's mental stats and can cause things to happen that they're not aware of.
I'll have to stop myself here, and point out the difference between an open roll, an obvious roll, and a secret roll, for the DM. An open roll is when the DM leans over and rolls the dice where everyone can see. An obvious roll is where they can be heard and seen rolling the dice, but the numbers aren't shared. A secret roll is done before the session starts. Just roll a bunch of dice for people, and mark a chart "Your first roll was an 18, your second was a 3, your third a 14..." and use those when the players should be unaware. Like, when a thief enters the room, you don't say "roll perception" because then the players know that SOMETHING is up. Instead, when the thief enters, you already have a pre-rolled number, and then modify it by the player's perception. The players don't roll anything, so they don't know the thief is there.
In the case of an evil ring changing someone's actions, do some secret rolls for will saves. As they walk through town, every fail on will is an evil action the player and character aren't aware of. Like, they're walking through the market, and then when they get back to the inn they realize that there's $500 worth of exquisite robes stuffed into their backpack, that they'd stolen under the ring's possession without being conscious of it. This can also lead to hilarious self-doubt. "The locals say you killed the farmer." "You know I didn't!" "Well, we found a human hand under your bed..." which can then make the players think they've been set up and framed, when they actually DID do it, or at least were possessed when their body did it. If this is done to a paladin, it can be hilarious, as the upstanding faith collides with unknown evil acts.
To compensate, the ring could be powerful and not make the player think they need to remove it. Like, if the character falls below 1 HP, once per day the ring will automatically cast Cure Light Wounds as a contingency spell. Or if the character suffers a critical hit and it is confirmed, the ring automatically casts Quickened Dimensional Door and transports them 10 feet back to automatically negate the hit, once per day. It could provide different benefits depending on the scenario, the specific setting might make poison immunity into a very valuable tool, or fire resistance. IN PARTICULAR if it's a defensive action, then the player will love the insurance. If the ring performs something exclusively offensive, they may feel that they can get better use out of a different choice of attack and try to discard the ring.
Another REALLY interesting idea, I've wanted to try more on myself, is that the item is a phylactery, of sorts. That is, when a lich is slain, their body simply regenerates at the location of their phylactery and they recover with no lasting penalty. This particular item is more of a 'conduit' than anything else. The lich has simply cast himself into the astral plane, and anyone who wears the ring slowly becomes consumed by the lich's power, until the lich takes over completely and the character becomes an NPC. The BBEG could have been that lich, or could have been using the ring as research material or communicating with the lich. Meanwhile, now that a player character wears the ring, he'll suffer bouts of memory blanks, unusual evidence appearing around him, and disjointed reality that leads to a the conclusion that he's doing these things, even though he KNOWS he's not doing them. If you've ever seen Fight Club, that'd be a good way to handle things. Either way, the player has to realize what's going on or be told what's going on, and THEN has to go through another campaign to break this curse.
Anyways, even if you don't do these things, the two ideas. Make it subtle, so that they wouldn't think about discarding the ring (although it's cursed, they can't get rid of it anyways!) and make your dice rolls more secret and more controlled.