I have used Toggl (now Toggl Track) for years and really like its streamlined design and simplicity. In my experience, it interfaces very well with Asana, allowing you to start timing a task by clicking on a Toggl button either within the task details or directly next to a task in the “My Tasks” list. Projects and users can also be synced automatically (this is a setting within Toggl). I have always used the free version, which I found to be completely adequate for tracking time with Asana. You can compare the features and prices for the other versions here: Pricing | Toggl Track.
One downside is that the time spent on a task does not get imported automatically into Asana, though I’m not sure whether any time tracking app is integrated in a way that allows this. The other main downside is that I’ve experienced a few glitches from time to time in the project not being selected automatically in Toggl when a task is started from Asana, but this is something that the Toggl team has resolved fairly quickly each time this has happened.