Questions for the audience about course management systems

I’m pretty busy right now with writing, administering, and grading midterms — so blogging is light for a day or so more. However, given the recent posts and traffic about course management systems, I wonder if you wouldn’t mind answer a few questions down in the comments area. 

1. Teachers: What do you need a course management system to do? What functionality do you consider essential?
2. Teachers: What are the best ways for a course management system to help make your job of managing a course easy?  
3. Students: Same questions as #1 and #2. 
4. Current CMS software users: What are the three features of your CMS that are the most essential? If you could change three things about the way your CMS works, what would they be and what would you rather have?