Two occur to me: Chell from the Portal games, and Lufia from Lufia and the Fortress of Doom. And both of those almost don't count.

I almost don't want to count Chell because she's almost not a character, but I've had quite a bit of fun playing as her.

Lufia is one of the rare SNES JRPGs not made by Squaresoft or Enix, it was published by Taito. Gameplay is similar to classic Final Fantasy, the story manages to be quite tragic. Lufia, the title character, is not the player character, Enter Your Name is the player character, and Lufia is a playable party member/his love interest/...well, play the game to find out. So there's reasons why I hesitate to call her a "protagonist."

I have to mention a fun thing that series did: Lufia 1 starts with a playable prologue/tutorial section where you play as some legendary heroes fighting an ultimate battle. Lufia 2 is a prequel, and it's the story of those legendary heroes, which ends with that same ultimate battle as the final boss. In Lufia 1, the heroes speak very formally. They sound stalwart and brave and a bit old fashioned, as legendary heroes should. In Lufia 2, we know these characters more as real people, and the dialog treads the exact same ground but it's much less formal, makes them sound less hypercompetent.