In Outlook 2010 (on my To-Do List -- the default view when I click the Tasks button in the left sidebar), I only want to see tasks, not flagged e-mails. Is that possible?
Yes, you can create a filter. When you select Tasks, and with your To Do List selected, click on View in the ribbon (at the top) and then click on View Settings.
From here, you can filter.
For your need, I think you'll need to use Conditional Formatting where you can unselect read and unread emails.