Recs.
Updated
SpecsUpdate
Pros
Pro Very polished interface
Teams can have private (only visible to project members) and public (visible to anyone in the team) projects. Each member can also have their own personal projects.
Tasks can be viewed in list and calendar views. It's possible to display only the tasks assigned to the user or tasks organized by project or team.
Lists of tasks can be divided into sections and organized in many different ways - tasks that still have to be done, tasks that have been completed, by due date, by assignee, by popularity.
Single tasks can exist in multiple projects.
Expanding a task will allow adding things like subtasks, tags, attachments as well as leaving comments and subscribing to a task via RSS.
There's a separate view for attachments.
Search for finding stuff quickly.
Pro Simple workflow
The Asana task workflow within a project is broken down into "Today", "Upcoming" and "Later".
The tasks themselves have the status of either done or not done. There is also a sub-task feature to group tasks together.
Tasks can be assigned to each other and are stored in the "Inbox" view for processing. This replaces email for some team communication.
Cons
Con Its not built for projects
Simple todo list, not very good for projects.
Con Sluggish website
Asana uses their own Lua framework which isn't really optimized and takes quite a long time to load. The developers of Asana have started working on a faster version of their framework - Lua 2 - that will be used and implemented in 2016. The website however still remains somewhat sluggish.
Recommendations
Comments
Out of Date Pros + Cons
Con No free plan
There is no free plan like for personal use and the minimal cost of $19/month might be prohibitive.