Yes. Here is a 'list' of what Friendship can determine:
- The Power of Return and Frustration, which reach a peak of 102 Base Power.
- Some Pokemon evolve by happiness. If a Pokemon has a high enough happiness level, it'll evolve upon next level up.
- Move tutors sometimes require a Pokemon with happiness to teach a move, e.g. Draco Meteor.
- A few ingame Ribbons can be obtained upon high happiness.