Alt+Tab works great for flipping between proper applications, but what if I want to see all the little icons by the clock and I don't have a mouse? Is there an alt+tab equivalent for the system tray icons?

Win+B will move focus to the System Tray icons. You can then use the arrow keys and enter to move between and select them.
For more info you can check "The Master List of New Windows 7 Shortcuts" over on LifeHacker.com.