Wunderkit has everything you need, and more. (I personally use its stripped-down version, Wunderlist, for personal tasks - make sure you check it out as well.) Wunderkit is a perfect tool for collaboration (sharing tasks and workspaces, commenting, tracking team progress), but also works flawlessly for personal task management.
Here are some of the features (I think these cover each and every requirement of yours):
- Workspaces (that is, separate spaces for projects)
- Tasks (tags, assignees, due dates, recurring tasks, comments, starring)
- Notification-type badges for tasks due today
- Notes (also with tags)
- Syncing between apps
- Available for Mac OS X, iPhone, and as a web app
I expect the app to be available on more devices soon. I base this assumption on the fact that the before-mentioned Wunderlist is available on iOS, Android, Blackberry, WinPhone, Mac OS X, Windows, and Linux.
Oh, and the best part: it's wonderfully designed, and it's free.