Bug 1179596 discusses various user agent string options for ubuntu phone browser.
I was able to get mobile yahoo mail app going by using my personal user agent string variant derived from the firefox android one:
Mozilla/5.0 (Ubuntu like Android; Mobile; rv:13.0) Gecko/13.0 Firefox/13.0
Do you have a website that doesn't work well on todays daily phone image, but that you can make work with a user agent string similar to the one above? If so, please leave a comment.
p.s. you can hack the user agent string at your own risk in /usr/lib/arm-linux-gnueabihf/qt5/qml/Ubuntu/Browser/UbuntuWebView.qml
Edit: as of Jul 11, 2013, the path of the file above has changed on the device to: /usr/lib/arm-linux-gnueabihf/qt5/qml/Ubuntu/Components/Extras/Browser/UbuntuWebView.qml