Tony Ruscoe of Google Blogoscoped reports that Google Gears alert messages indicates that support for Gears offline access to Google Docs is forthcoming. As Tony notes, the "the only official Google Integration is for Google Reader (although evidence that offline functionality is coming to Google Calendar has also been spotted)."
Here's one example from our mashup directory, the personal finance site Buxfer that lets you auto-sync your banks and credit cards but also uses Google Gears to let you store your personal finance data locally in a Gears database instead of a Remote Server.
Google has representative examples that show off the synchronization and coding model. The Google Gears blog has examples like the application suite Zoho, along with an offline editor for Blogger. On the Salesforce.com developer site there is an extensive tutorial for using Gears to access account data. And here's a mashup example with Gears and the Digg API that can capture Digg stories for offline viewing.