This whole thread is quite funny to read, very strong opinion for and against...
Here something ..
I understand from the question that it was technology agnostic and not bound by time. Thus current development in silicon, quantum computers or the Infinite Monkey Peddling Abacus are in effect irrelevant.
Calculations and extrapolations are also quite funny, though the answer from back2dos works quite well to illustrate the sheer size of what this number represents. so let's work with that.
Put your mind in the future where man is no longer bound to the confine of it's little planet, a realistic means of transportation was developed to allow transportation over very large distances and the social structures (economic, political etc) have evolved to transcend generations. Pharaonic projects spanning have become common places. Let's focus on two aspects of this far fetched vision of the future yet, should one wishes to spend to time to explain every details I'm quite certain one could rationalize all of it through a series of plausible evolutions on current technologies. In other words a plausible, albeit unlikely future... anyhow...
The first project called Colossus in memory of that first electronic computer as it is the first planetary computer. The Colossus Brotherhood has indeed figured out a means to capture a small planetoid and transform it into a working computer. Recently discovered in the Kuyper belt that is perticularely rich in fusible isotopes making it energetically autonomous, they made the construction process completely autonomous with probes, robots etc making the computer system self repairing and self constructing. In this condition it would be conceivable that 2^64 address space being somewhat confining for this project as they wish to get a continuous address space to easily port applications already existing for another project also under-way.
The other project is more of a an experiment in networking than a physical system, yet, it quickly demonstrated that larger address space were needed. 540 years ago a young hacker was toying with the idea of creating a gigantic bot net. The internet had already expanded to include the nascent colonies around the solar system building on major advances made in fusion power. His ideas was basically to have little bots spread around the network but the payload was destined to provide a unified virtual machine where code would be written assuming it had all the power of all bots combined. Great efforts were put in the compiler and deployment attempting to optimize lags and sophisticated algorithms designed to take into account the inherent unreliability of the underlying medium. A language was specifically written to target this new "computer" that put major emphasis on concurrency. It took many years to discover this botnet since it never delivered any attacks, our hacker created instead an umbrella company and sell the computing power to the highest bidder. When he died he donated this botnet and all technologies to a foundation. At that point the botnet had already been running for 64 years and had already outgrew the 2^64 address space quite a while ago shattering the 1000 year old preconception that we would never require larger address space. Nowadays 2^128 is the norm and what will be used for Colossus but there is already plans to expand this to 2^256.
I could probably come up with more quasi plausible scenarios that illustrate that yes... it is quite possible, nay, almost certain, that one day we will require address space larger than this.
That said however I do not think I would loose sleep over this, if your application requires a certain address space to work correctly then most likely it will live in a VM that gives it all it needs...
Thus... short answer...
YES, Most likely
but
Why not deal with this when the problem comes... Personally I never make assumptions in my programs thus never get surprises.