Because this is difficult, here are some answers with differing criteria:
Playable: Zero from the Mega Man X series - He's the character you use as a metric to see how much X improves over the course of the game. In all reality, X is pretty much Zero's sidekick at the start, and it's rewarding for the player to slowly become even stronger than him. He isn't playable until X3, and not fully playable until X4, so this isn't really the most accurate category, but oh well.
The lesser character of a duo: Kazooie from Banjo Kazooie and Tooie - Banjo may be the head honcho, but he wouldn't have any of his best moves without his cocky feathered friend. Kazooie is unapologetically abrasive, and makes the games more humorous as a result.
Frequently influences gameplay, but isn't playable: Elizabeth from Bioshock Infinite - She throws you resources, can alter reality, and has a lot of depth as a character. She might seem like yet another damsel in distress at first, but you'll quickly learn that she's a very determined and handy young lady.
Doesn't largely influence gameplay: Alyx from Half-Life 2 - She's strong-willed and likeable, as well as cute without being sexualized.
Is playable in a limited sense: Epona from multiple Legend of Zelda games - In Ocarina, Epona is extremely valuable; nobody wants to walk across Hyrule Field every time, and she's the solution. All it takes is a quick song on your ocarina, and presto, there's your faithful horse. She's not nearly as handy in Majora's Mask, but still great as a companion for story reasons. I haven't fully played Twilight Princess, so I can't speak for her presence there.
