A few people have suggested timelines before (ie, Gantt-style views, or timelines that deliberately are not Gantt-style). I have a suggestion that is two-fold, and is a little different than the previous suggestions.
First, to provide an alternative Calendar view that is not based on the traditional calendar layout. Instead of columns of days, with rows of weeks, a view that is just a single row spanning a period of time (horizontal scrolling, of course) would be very helpful. Combine this with a zoom level, and allow us to view that timeline as days (each division is a single day), weeks (each block represents a week), or months. For projects that are used as multi-project planning lists, seeing this level of view would allow for very fast high-level planning.
Second, it would be great to also have the option to show a calendar/timeline of a consolidated view of multiple projects. Not all projects, just selected ones. Then you can have a single calendar view and pick 2, or 3, or more projects, and have Asana consolidate the overall deliverables of that project into a single view that summarizes the contents of the smaller project. It doesn’t even need to be real-time data (ie, caching and hourly refreshes or something similar would probably suffice). This way, the earliest “start time” extended to the latest “due date” would simply be presented as a calendar item that summarizes an entire project in the consolidated view. It would be great for automated high-level planning.