It didn't really work for me as a personal organiser. Paper was just too damn handy, didn't require a log in and I didn't need any of the collaboration features. It didn't work for my dad and his business because he didn't quite 'get' the task oriented nature of the beast and ended up with a weird mish mash of orders, inquiries etc which ended up being unmanageable and he abandoned it quietly.
I tried setting it up for the production pipeline at the video society at my uni. I thought it would help lower the barrier to entry so that people could more easily get involved, see what was in the works, see tasks that were available to contribute to. But no, nobody logged in. The motivated people were just motivated and didn't require any task management and the disengaged people were too disengaged and uncurious to find it a useful resource.
I tried setting one up at my internship - a small data shop where surely things could be easily captured as tasks. We could assign things, hand things over, track bugs in code, split up larger assignments into smaller ones. But again, after some initial curiosity and a lot of patience from the teams, it didn't quite take either.
It feels a bit like the slow rise of corporate instant messaging generally or slack more specifically. Tools can enable a massive improvement to an organisation's ability to keep in touch, react to change, collaborate and all that usual stuff, but unless the company embraces that change or has a mindset/culture that allows those benefits to come to fruition then even with something like Asana you won't be able to turn things around with tools alone.