Will the mobile phone overtake the computer for web access?

What a great question, its a shame the answer is quite simply yes and that has already been shown. All you have to do is walk around any college campus these days and you will see that the mobile phone is all most students utilized for web access. Based on the smart phone apps that are available most phones are the only means this demographic has for web browsing. They are already dictating the future of web browsing and all computer companies have begun to capitalize on this through their attempts to create smaller lighter and faster laptops. Mind you I said laptops since the majority of desktops have begun second pick to the laptop.

In my opinion, the whole idea of the "mobile phone" has evolved so much that they are better and increasingly referred to as "mobile devices". That said, I do believe that mobile device internet access will certainly overtake traditional desktop and laptop systems, especially given the expected wide adoption of tablets. In fact, I'm surprised mobile computing hasn't already overtaken computer access.

Further, these devices will likely be the primary means of internet access in developing countries and emerging markets around the globe where infrastructure and economic constraints make traditional desktop computers more difficult to obtain and support. Mobile devices are far less expensive, generally more durable, and require less constant and stable energy sources which can be a big deal in developing nations.

Mobile Phone web access will increase but i don't foresee it overtaking Computer Users.
In developing or Under developed nations the use of Computers is much more than Mobile and it will remain the same till infrastructure for telecommunication is developed.

There are two statistics one must look at. One is "time spent" on the Internet, and the other is what is the most common method of "access".

Mobile will easily by far become the most common device to access the Internet, but it won't lead in "time spent".

So in the future, you have to take that into consideration because people use mobile internet for different reasons than they would use computers, tablets, e-readers and other forms of connectivity devices.

I believe it will... as we move towards Secure Cloud Computing space.

Mobile networked devices such as smartphones have already outstripped traditional PCs and laptops for Internet/Web access in many localities. This is especially in developing countries where computers are more expensive, and in areas where mobile broadband is already or is becoming the "go-to" connectivity method. This is a trend that will increase, and mobile networked devices will gain functionality that makes them increasingly competitive with traditional computing devices for access and for "time spent," as Dan Verhaegae said.

Yes - for a few reasons... in priority order
#0. Mobile phones are always on and always with us and they enable:

#1. Social networking. A lot of people (esp. young gen) already live in this way
#2. All personally important information available online at all times - ranging from weather reports through stock options to job offers
#3. Business. The most of the progress to be made in this area - it's going to take time, esp. for large organization, to provide secure access to the legacy applications through the mobile devices.