There’s a special mode that web pages can select when being added to an iOS home screen, where instead of running in Safari they will appear to run in their own full screen mode. Very few pages seem to bother setting it, including ones that would be nicer if they did, so I’ve created the following bookmarklet which lets you force any web page to support this mode.
The tricky bit is getting the bookmarklet onto your iOS device in the first place. The only way I know to do this currently is to add it to your Safari bookmarks on a OS X or Windows and then synchronize these with your mobile device using iCloud. Whee!
Assuming you’ve managed to add it to your Mobile Safari bookmarks, simply select it while viewing the web page you want to appify just before you “Add to Home Screen” and it will add the requisite metadata to the page, allowing it to be presented as a full screen web app (once launched from the new icon). To illustrate the difference it makes, here are screen shots of the same page running in regular mode and web app mode respectively.
Some pages will suit this treatment better than others. Since web apps are not allowed to change their addresses, clicking on an external link will generally pop you back to Safari again, unless your page is doing some clever ajax-y stuff, or is nested inside a <FRAME>.