Ubuntu 11.04 Natty Narwhal will get overlay scrollbars but for now the packages that provide this are available in a PPA and further more, you must use "export LIBOVERLAY_SCROLLBAR=1" when launching an application to get overlay scrollbars.
But there's a way to launch all applications (apps which support it - not all applications will work!) with overlay scrollbars by default.
Firstly you'll obviously have to add the PPA I was talking about and install the required packages:
sudo apt-add-repository ppa:ayatana-scrollbar-team/release sudo apt-get update sudo apt-get install liboverlay-scrollbar-0.1-0
Then, to get overlay scrollbars for all applications by default, copy/paste the following commands in a terminal:
sudo su echo "export LIBOVERLAY_SCROLLBAR=1" > /etc/X11/Xsession.d/80overlayscrollbars
Then restart your computer (logging out doesn't seem to be enough).
Update: here is a video demoing the new overlay scrollbars (you can also notice that the overlay scrollbars work with any theme) - video thanks to deadite81:
Thanks to Georgi for the tip!