Interest in HTML5 is definitely hotting up-and not only from within geekland. Leading corporates are keen to "something different" that hasn´t been before, and HTML5 is definitely flavour of the month.
There still are several issues with HTML5 that mean that its adoption has been limited or, at best, what has been adopted were the "easy bits" of HTML5 that are more stable than the more racy components (the location component, for example).
Specifically in terms of mobile browser adapted sites, the examples are even thinner on the ground. The Financial Times´s recent move to switch from a native iPhone app to a HTML5 site instead could be seen as a watershed event.
However, while HTML5 is great for showing content, clearly it is not a replacement for native apps which call native features of the handset (camera, accelerometer etc). Can you make an image in an HTML5 mobile site animate when you shake the phone...no, you cannot (and yes, some clients ask for it!).
You can see a great comparison by Michael Mahemoff of some pros and cons of developing native vs HTML5 apps here: HTML5 vs Native apps comparison. Overall, the point is that web apps are closing the gap on native apps..this is true in many ways, but then the gap in some cases was very large.