Ubuntu Software Center will have Zeitgeist integration in Ubuntu 11.04 as announced by Michael Vogt on his blog. Seif Lotfy, from Zeitgeist Developers' Team proposed the idea of possible integration of Zeitgeist into Ubuntu Software Center.
Excerpt from Michael Vogt's Blog:
Seif Lotfy committed a nice zeitgeist integration branch for software-center here. I’m pleased to say that it is now fully integrated into software-centers trunk bzr branch. It won’t make Ubuntu 10.10.10 but when 11.04 opens, it will be one of the first new features.
What is Zeitgeist?
Zeitgeist is a service which logs the user's activities and events (files opened, websites visited, conversations hold with other people, etc.) and makes the relevant information available to other applications. It serves as a comprehensive activity log and also makes it possible to determine relationships between items based on usage patterns.
As of now, it will log the number of times an installed application is used in Ubuntu. But more ways of Zeitgeist integration will come in future. (Screenshot from Seif Lotfy's Blog)