Google made Google Calendar and Doc accessible from Gmail. To show the Google Calendar and the Doc widget in Gmail, enable Google Calendar and Google Docs gadgets from Gmail Labs.
Google Calander Gadget : Gmail Labs
Google Doc Widget : Gmail Labs
By default the widget will display in the bottom of left column. If you will use Google Calendar widget as a reminder window then the chances are high of missing events as the widget will not be visible untill you scroll the page.
There is one more gadget available in gmail labs which can enable you to re-order Navbar. The name of that gadget is Navbar drag and drop. After enabling this gadget you can drag and drop Google Calendar widget (or any other) above the chat widget so that you can see the upcoming events.
Navbar drag and drop gadget : Gmail Labs
