The ability to changing the world is what draws me to a gameworld. Birthright has that in spades. The ability to play the head of a kingdom is inspiring. The best part of Birthright is that along with playing the leader of a nation, a character can be the head of a thieve's guild, control the magic in a region or be the head of a church that sways the mind of the populace. I like this because it allows for diversity of play styles; you can be a thief while still affecting the world.
Birthright also allows for multiple players to integrate their leadership roles into a cohesive whole. Instead of one player character "ruling" the other player characters, they can actually work together with common goals they can share. They can do this while still being individuals. The ability to mesh personal drives, and play styles while retaining the party mentality is a major strength of Birthright.
Birthright also has a rich back-story and history that is engaging and an excellent catalyst for adventure, both for the typical "dungeoneering" variety and the "lead nations" variety. The villains are great - they are devious and deadly as well as being unique. There are also world mechanics in play such as Bloodlines.
Overall, I always enjoy running Birthright.