There are officially more cell phone users connecting to the Internet than PC users in Japan as of 2005 according to this government report found via Wireless Watch Japan.
69.2 million people using the Internet from mobile devices, compared to 66 million conventional PC users
I spend much of my day connected to the Internet through my laptop, so it's hard for me to relate. I wonder what percentage of Internet sites, services, and resources have migrated over to cell phone compatibility in Japan. I also wonder what the likelihood is of this occurring in the US.
In terms of connected games, a population that's this comfortable accessing the Internet from their phones would probably love the chance to interact with their favorite virtual worlds/identities with their phones. Then the question would be whether these connected games are the end state or just a waypoint in the transition to cell phone only.
I don't think people will abandon PCs in the near future. PCs offer major advantages, like larger screen size, better hardware and software interfaces, faster speeds, greater storage, etc. However, I can envision cell phones catching up on speed and storage in the next decade or two. A great voice interface could replace much of the awkward key pressing, or to venture further into sci-fi we could use our minds directly to control the devices. Or maybe everyone just uses styluses. And it's not too hard to envision a pair of light weight glasses like the ever elusive comfortable virtual reality or augmented reality headset that could augment or replace the tiny screens. Will we still need PCs?
Answering that question hinges on defining PCs. Laptops are considered PCs because of the similarity of features. PDAs/smart phones are usually not, and have different capabilities. But as laptops shrink and smart phones get more capable it may no longer be useful to distinguish one as PC and the other as not.
East vs. West
I think there are a few reasons why we in the West may be more reluctant to give up our PCs than those in the East (Japan, Korea). First, the cell products we have in the West are just not as compelling. The hardware isn't as good, the services and applications aren't as good, and we have much worse land area coverage because we're much more spread out geographically. That physical dispersion means that we each have more space to ourselves (bigger houses) making our personal space more comfortable than in the east where people are more tightly packed. It also means that it's less convenient to go see other people than it is in the East where people are, again, more tightly packed, so we stay home more. Cell phones are not the best entertainment devices when we are sitting on our couches or at our desks, so we invest more in big screens (less mobile, obviously).
I don't claim to understand all of the ramifications, both positive and negative, of games merging more closely with reality, but for a preview we should look at alternate reality games and augmented reality games.