OpenOffice formats are supported by Google docs. (Thanks, Google!)
Getting Data From OpenOffice.org Into Google Docs
You can copy and paste into a new blank document, of course.
You can click the Upload tab and get this window.
And there's a nice little extension for OpenOffice.org that when installed will give you a menu for uploading your docs to your Google account.
Getting the Data Out Into OpenOffice.org Format
When you're editing a document, there's this option.
In the main window, there's this option.
Getting Other Google Contents Out, to OpenOffice or Other Formats
This blog shows how to get your Google content for Google docs as well as other Google web apps like AdSense.