iPhoneBuzz has coverage of Vic Gundotra, VP of engineering at Google, demonstrating a Gmail webapp that also functions offline. The webapp is running on the next version of HTML, known as HTML 5. Any browser that supports HTML 5 will be able to run apps like these that work both online and off. HTML 5 will allow for webapps to read/write to a database (ie, an email inbox) on the phone. A webapp can also save a copy of itself in an executable state on the device.
In the video, they show the Gmail webapp working in airplane mode on an iPhone and on a HTC Magic G2 Google Android phone.
(Via iPhoneBuzz)