The percentage of people with mobiles browsing the web is going up sharply, due largely to the rise of feature-rich smartphones. According to ABI Research, around 130 million people now carry phones that have what we'd call “modern” browsing, and within the next 4-5 years that's expected to quadruple.
The research primarily points to phones from the likes of Apple and RIM, along with the expansion of 3G networks that offer speeds worthy of web browsing. Many sites tailoring to mobile users have helped as well, with Google definitely leading the pack for making a vast array of services functional and even easy to use on a mobile.
There are a lot of hurdles to get over. Even the fastest of 3G networks on fast phones pale in comparison when pitted up against the speed advantages of an actual broadband Internet connection, and viewing all your content on a three inch screen can get tiresome after a while. Cellular speeds haven't improved anywhere near as fast as Internet speeds either, which compound some of the issues – but people are still open to it, and manufacturers are still trying.
From my own experience, even a single generation of smartphones can make a night-and-day difference. I wouldn't be surprised to see Netbooks all but supplanted by sufficiently powerful smartphones, with people relying on them for hosts of applications, all types of communication and of course web browsing.