My favorite is still Cortex Dramatic Roleplay*, the system introduced in the Smallville roleplaying game.
I love the way it models the back and forth nature of relationships with the way your relationship to someone can get stronger or weaker as you play, and the nature of your relationship with each person changes as you learn more about them and interact with each other. I like that relationships and personal values have mechanical weight. I like that it forces you to decide who and what is important to your character and your relationships and motivations are the dice you roll to accomplish anything you need to do.
I also like the mechanic where you can challenge a relationship or value. Each relationship and value has a statement. For example:
d8 Anna - "Anna is my most trusted friend."
d10 Truth - "I can't let anyone find out the truth about my inheritance."
I really like that part of the game, where your character grows by interacting with other characters, by caring about them and sharing scenes together, building drama and interpersonal relationships.
*But boy does the Alien game have a great mechanic for losing your shit when you're scared!