I’ve used them occasionally to good effect. Some of the various plots/machinations for when they’ve showed up ended up appearing on my d100 Encounter Activity Table for them: OSE Encounter Activities - Doppelgänger (d100).
One method I took when running them ages ago was pretty devious: This worked rather well with a group of five player characters (even if it’s a little on the Low Trust side). Doppelgängers were featuring very heavily in the story up until this point and before a major scene in a palace addressing the King and Queen, I made a very loud production of pulling each player aside and speaking with them for a few minutes.
I asked each player individually during this time if they would be willing to play a doppelgänger version of themselves for this session, assuring them that their character’s would be completely fine, and that they could very well garner some extra XP for the session. Naturally I also mentioned that this would have to be done rather secretively to maintain the illusion, and any table talk could potentially ruin the surprise. I arranged different signals with each player to reveal to me their decision and my response at the game table. One player was to get a can of Soda out of the fridge and set it upside down to signify that she was willing to play the part of a doppelgänger for the session, and my response would be to tell them to flip the can over if yes, ask for their Charisma score if no, and ask them for the pencil sharpener if I already had a doppelgänger. Insidiously, I also mentioned to another player that their signal for providing their answer also involved the pencil sharpener, and that I would ask for another player’s Charisma score if my answer was no. The signals were intentionally rather round-robin in this fashion to help generate the requisite amount of paranoia at the table -everyone was looking for very similar signals.
Once each player had been taken aside and informed of this, I returned to the table and mentioned off-hand that I had asked everyone pretty much the same question, and that we could begin.
Each player was completely on edge as soon as the signals started flying back and forth. I knew that I wanted to avoid a lot of note passing between myself and the players, so these signals did the trick without “outing” any potential doppelgängers to the rest of the group.
It turned out that only one person was actually up to the challenge of being the doppelgänger, but I used their signal to let them know that I already had one, so each player ended up spending the entire session absolutely convinced that one of them was a traitor in the ranks. It was a very fun session, and everyone received plenty of XP.
They occasionally still pester me about who the doppelgänger was during the session, but I’ll never tell. I just respond that the player that played the doppelgänger was sworn to secrecy, and would probably categorically deny it if accused, or risk forfeiting the extra XP.