Most of the answers in the above question seem to be addressing how many followers you can get through normal means. However, I've recently noticed a bit of a bug in the quest follower system that may allow you to gather a small army.
During one game recently, I had Trinity Restored in my quest list. I was at the step "Meet Karliah at the standing stone". Before doing this though, I decided to take care of some other things I'd been wanting to do. One of these things ended up bringing me near Riften, in the area of that standing stone. I ended up passing close enough to Karliah and Brynjolf to trigger the next step in the quest. At this point, Brynjolf begins following the player.
I didn't realize I was being followed until later on, far from the standing stone, I heard Brynjolf speak up. I double-checked UESP to see if he was essential (I don't need to be getting him killed before I finish Trinity Restored, after all) and he was. So, I just decided to continue having him follow me. He continues to follow me for now, everywhere I go.
The other task I've been doing, is collecting all of the Dragon Priest masks. One of the masks can be obtained during a quest called A Scroll for Anska. As soon as you start this quest, Anska also becomes a follower. She will also follow you out of her dungeon into the open world, but doesn't seem to want to wander far from there. (I tried fast-traveling to Riften, and seemed to lose her then. She began following me again into the crypt when I returned.)
Still, I'm wondering: How many followers like Brynjolf (who will follow you to the far reaches of Skyrim, while allowing you to add other followers) are there out there? Could they all be joined together to form a bit of a posse, as long as I do not complete their quests?