Is there a maximum possible voltage?
First of all: voltage has nothing to do with distance as some people say. Electrical field has to do with distance, but voltage is simply a potential difference. The highest voltages can be reached with so-called bulk charge, i.e. the amount of electrons in a certain mass of matter divided by the mass of the object. 

Yes, there is a theoretical maximum potential difference. It is the potential difference as dictated by the Pauli exclusion principle; i.e. no two particles may exist in the same state at the same time. This limits the density of electrons that you can have in the universe and, conversely, the maximum potential difference. It may be possible to construct such an electron-dense cloud synthetically for an infinitesimal amount of time even, although it would obviously never be stable. Protons are a suboptimal way of (theoretically) constructing a potential like this, as their charge density is many orders of magnitude lower. Bare electrons are the way to go as the lowest-mass charge carrying particle in matter**.

Now, this says absolutely nothing about the upper limit on a practical, (pseudo)stable voltage. There is no such thing as a maximum density electron cloud and more importantly, it's very hard to produce a perfectly neutral counterpart close enough to do anything with. We know that neutron stars are essentially the densest 'usable' matter in the universe, but it is electrically neutral for the most part (although it probably has a soup of charged particles living on quantum degeneracy pressure in the core). It's probably a bad candidate for a really electron-dense piece of material. 

Black holes are another big problem for the practicality of things. We simply don't know what actually is a black hole. If it's a true singularity (i.e. all matter concentrated into one point), it is an exception or extension to Pauli's exclusion principle and when viewed just in the three dimensions of space it can be regarded as an infinitely dense object. But we also know that it probably has no charge at all, and even if it did, the electromagnetic force cannot interact with anything over the apparent horizon. So this is probably also not a candidate.

The next and probably 'best' candidate is most likely radiation-stripped hydrogen gas clouds. It's not dense at all, but hydrogen clouds around highly active star-forming regions are constantly being stripped of their electrons by the intense x-ray and ultraviolet (ionizing) radiation from young, blue, bright stars. This means we're dealing essentially with a big cloud of protons. Downside is: electrical interaction is hard, so you can't do anything with that potential, but it's there.

** I forgot quarks.. I guess you can be even a bit more efficient with those.