Clementine, Thunderbird and gVim are some applications that I use and don't display overlay scrollbars.
InstallOpen a terminal window and run:
sudo apt-get install overlay-scrollbar liboverlay-scrollbar-0.2-0
ReferencesOverlay Scrollbars - Update @Canonical Design
Overlay Scrollbars on different toolkits @Blueprints for Ubuntu
Full Circle Magazine - Ubuntu 11.10 and Unity Special Edition, page 12