Google Gears now works on my Ubuntu 8.04 installation, at least almost. For Google Docs the little green symbol appeared after I had installed Google Gears for Linux. Then I headed to Google Reader, but there the symbol for offline support did not show up.
I do not know, what is going wrong, but my Google Reader just does not support Google Gears, somehow. I will keep on trying, but at least Google Docs work. That is one step ahead.
UPDATE: Seems like currently I am blogging too fast! I just added a new feed to Google Reader, and the little pop-up for activating Google Gears for this website appeared. It seems to work perfect.