If you are using Evolution you can display your Google Calendar events in Ubuntu's panel by using Indicator DateTime. However for one reason or another you might not want to use Evolution. Here comes Calendar Indicator, a new utility that helps you view your upcoming events in Unity's panel. Calendar Indicator is available for Ubuntu 11.10 Oneiric Ocelot and 12.04 Precise Pangolin in the Atareao PPA. To add the PPA and install the application, open a terminal and type:
sudo add-apt-repository ppa:atareao/atareaosudo apt-get updatesudo apt-get install calendar-indicator
Once installed, start it from dash by searching for Calendar-Indicator and enter your username and password. Don't worry about its security since your password is stored in GNOME's keyring.
An icon with the current date should appear in the panel. It will show you the next 10 events. Moreover it has a built in calendar which you can use to view the events for a specific date.
Since this is a new application there are a few features missing such as the ability to add or delete events or which calendar to display but I believe those features along with others will be added in the future.