With every Mac OS X I've ever used, hitting command-backtick (`) cycled to the next window. I just installed Mac OS X 10.7 (on top of a perfectly fresh 10.6), and command-backtick does nothing at all.
Did this feature go away?
This feature is still present (I'm using 10.7.3 and it works for me).
Go to System Preferences > Keyboard and check the keyboard shortcuts. In the list of 'Keyboard & Text Input' shortcuts you should see 'Move focus to next window' ⌘+`.
Make sure it is checked, and it should work.
You might also be interested in Hyperswitch.
Along with Command ⌘ + Tab ⇥, hyperswitch allows Option ⌥ + Tab ⇥ to switch between windows of the same app. I find it much more useful than Command ⌘ + ~ (tilde) since Command ⌘ + ~ (tilde) only iterates through all windows, rather than just toggling between two.