Our very favorite project management software. Everything you would want or expect in task management. Also, it is cloud-based, has mobile apps, keyboard shortcuts, now offers Kanban and Gantt views if that's your thing. Highly integrable. Too many features to even list, and they're constantly shipping new ones, all without overloading the UI and making the tool clunky.
Not a good place for highly structured customer data. Keep that in your CRM and link to it from Asana. Asana is also so easy to use that you tend to see lots of disorganization and mess, because you don't have to be so deliberate in setting things up.