Inspired by this thread on the Romulan/Federation Neutral Zone in ST: http://boards.straightdope.com/sdmb/showthread.php?t=372061
It’s an SF convention that interstellar empires would be like terrestrial empires – with clearly defined territory/space and clearly defined boundaries, only in 3D. Would that necessarily be so? Might not such empires interpenetrate? E.g., the Andorians colonize star systems Alpha, Beta and Gamma, the Terrans colonize star systems Gamma, Delta, and Epsilon, and Delta is actually closer to Earth than Aleph is, and in the same direction – and the habitable worlds of both systems support the same general ranges of lifeforms – but the Andorians have Alpha just because they happened to get to it first, and the Terrans happened to get to Delta first. Would that necessarily lead to any conflict just because each race has a colony within the other’s “space”? After all, the existence of Terran colonies in the Delta system would in no way impede the Andorians’ access to Alpha. Couldn’t both races learn to live with that arrangement?
Not if you want to have a plot.
Hmm… possible to translate this into a 2D representation via a set of islands? It is obviously possible to go from one Island to another without stepping on another island, but for tactical reasons it’s unlikely that I’ll allow you to have a place from which you can launch assaults from “behind” my defences.
If you have two empires with different environmental requirements, you can have even more interpenetration, since one can make use of planets the other doesn’t need. You can get an interesting conflict started if there was a sudden need for a resource only available on one type of planet.
Even without that, there would likely be star systems without habitable planets between two empires, so I can’t imagine anyone drawing a line - unless some future Galactic President wanted to send the Space Empire Guard to patrol to help keep out illegal aliens. 
I was actually thinking about posting just such an idea to the Neutral Zone thread. An analogous thing happened with European colonization. Portugese colonies in the New World were closer to both Portugal and Spain than most Spanish colonies were. Who got what chunks of land once the European powers expanded outside of Europe was pretty much accidental.
Of course, in real life, the first expansionist species in space would likely colonize the entire galaxy before another spacefaring race evolved. Given the “facts” of Star Trek, however, (several species of approximately equal technology colonizing the Galaxy from different starting points simultaneously) you would expect each nation to be roughly spherical in shape. The degree of interpenetration would depend largely on the density of colonizable planets and the proximity of the various home worlds.
Each nation would, of course, require free access to each of its colony worlds from at least on (and idealy all) of its other possessions. Whether this would be achieved by regarding each occupied planet or system as a seperate territory surrounded by “international waters” or whether each nation would be seen as a contiguous blob in 3-dimentional space with corridors and wedges connecting systems on the periphery would probably depend on the ability and relative cost of any nation projecting its force continuously along such borders and corridors. Even given Star Trek levels of technology, it seems unlikely to be cost-effective to defend empty space, but that seems to be the model the writers settled on.
It’ll depend on what your FTL technology is like. If FTL is convenient enough for any sort of practical commerce between stars, and especially if interstellar warfare is convenient, then you’ll want a compact empire, so that freighters and warships can easily move between worlds, to where the customers are, or where the fighting is.
Of course, what constitutes “compact” will also depend on your FTL tech. If the primary or only FTL mechanism is wormhole-like connections (as, for instance, in The Mote in God’s Eye), then those worlds will be “close” which have wormhole or jumppoint connections between them, which might not bear any resemblance whatsoever to their positions in normal space. If it’s based on some sort of faster-than-light, but constant, effective speed, as in Star Trek, then close worlds will be just as they appear on the map. If it’s so fast as to be effectively instantaneous to anywhere, then all stars will be “close”, and empires could have any shape at all.
And, of course, if FTL is impractical for commerce or warfare, then no matter what the distribution of a race’s colonies, it’d be hard to call them an “empire”.