A couple of quick links I picked up on this week..
Google has made updates to its mobile gmail, mentioned here – http://gmailblog.blogspot.com/2010/10/gmail-in-mobile-safari-now-even-more.html
Mobile Gmail is a great example of a mobile web app that acts very much like a native app.
And on a related note, Robert Scoble’s interview of Starbucks CIO which I got to from Daring Fireball where John Gruber picked up on the approach Starbucks have taken. For them, they see more and more people using phones and iPads in their coffee shops, so they are building everything in HTML5. As Gruber points out, iOS is doing a great job for the open web.