Paper Mario: The Thousand-Year Door had about 90 bages, if you included the partner versions of the badges as well. As of this post, SW has 107, not including partner versions. (If we were to include parter badges, it would be 270). The number of badges is still climbing, since the majority of our current badges are support ones and not attacks. We still have more attacks and support badges to make, so I won't be surprised if we hit 150.
Points goes to the first person to break the game through badge abuse when it's released.