<http://en.wikipedia.org/wiki/Mobile_ad_hoc_network>
The instability of the network requires a bit different approach to networking in general:
<http://en.wikipedia.org/wiki/Delay-tolerant_networking>
In short: you can do email, with high probability, but more often than not can forget about VoIP.
There are a lot of options, each with their advantages in different situations. It's not so clear cut. It can be fast or it can be slow. It can be stable or not. It very much depends on the particular network protocol and setup.
I agree that right now it's not going to happen, no matter how many different efforts there are out there. For it to really happen I think we would have to come up with a plan that would actually work, in terms of creating a massive world-wide mesh network. There would have to be a lot of consideration for things like security, DDoS mitigation, speed, standards and upgradeability.
If developing a viable mesh network for the task weren't tough enough, there would also have to be a plan for migration which is really the hard part. Getting everybody in the world moved over to a new network would be nothing short of a miracle.