Vehicles, or just buildings. A raspberry PI (to use existing hardware - not saying it's ideal) with a 40 dollar wireless adapter and the right software could function the same way. The difficulty is almost the same as traffic planning - while in large cities it would function beautifully, routing requests to the node in range under the least amount of load, you inevitably run into bottlenecks as you leave urban areas and/or approach more important servers such as Google. You'll have little chains of nodes in areas with lower uptake, or just isolated homes and offices, and rural areas would, as usual, be kinda screwed.
Some of the problems could be mitigated somewhat by switching large services over to a distributed system using more of the PI's memory, but getting network engineers to agree to a single standard for this would be a feat of engineering in itself
Having larger traffic concentrations with artery lines through to each city would kind of defeat the purpose entirely. And yeah, it wouldn't function nearly as well as land-lines, because you're introducing processing lag at each node.
I've reached the limits of my ass-pullery for this kind of thing, so I can't say whether we'd have dial-up or even telegraph transfer rates. Difficulty aside, if this isn't resolved, confidence in dealing with financial transactions and business over networks could obviously take a serious hit as we march inevitably towards the NSA becoming an organization for petty thievery and prankery, harmless on the individual scale, but draining the world dry one Steam transaction and sext at a time.