To answer this, I'll refer to the Middle East, around the Mandate period in the early 1900s - bare (bear?) with me!

Essentially, the territory that the Mandates for Britain and France that were established post-WW1 cut through areas that had previously been associated with cities in order to create nation states.

For example, the hinterland around Damascus, which had the farmland to support the city, was split between Syria, Lebanon and Palestine. Each major city in the area, Jerusalem, Baghdad, Jaffa, would have a similar hinterland comprising of smaller towns and villages that supplied them.

Prior to the Mandate period, the Ottomans had split the Middle Eastern area into provinces by these townships, so there would be a Damascene province, a Jaffa province etc. As such, it can be inferred that the areas of control were based around cities not territory.

Since the Ottomans had controlled the region for centuries, and had continued the previous methods of administration (to a degree), it is safe to assume that this method of control over cities was a constant through history, as opposed to a territorial control.

Whilst I can't authoritatively state this, I would assume this to have been the case across Western Europe too, at least.

Sources: James Reilly's 'The Peasantry of Late Ottoman Palestine', the Sykes-Picot Agreement and Phillip Khoury's 'Syrian Urban Politics in Transition...'

Edit: Some grammar

I can give you an answer for Rome. Long story short: it depended on who was talking and on which time period we are considering. Throughout the Republic, the word provincia referred not to a place but to a task (see Rchardson: Hispaniae who refers to Livy's use of the word throughout his history). This boiled down to sending armies against peoples when it was necessary, not sending them to territories to keep them. Over time it morphed into the latter style.

That isn't to say that the Romans did not have a sense of geographical boundaries to an extent. In 509 BCE they signed a treaty with Carthage not to trade goods west of a certain point (Polybius 3.22). And of course they held the Rubicon as Italy's northern border in the time of Caesar. However, these boundaries rarely worked in practice. Cape Bello only worked for a sailor, someone in the interior of Africa would not know when he crossed that point (not that any Roman would be traipsing around that part of Africa). And in Spain, which was often home to two Roman commanders, the proconsuls/propraetors often bickered about the extent of their commands and often crossed the theoretical boundary between them, again because it was more useful on the coast than in the interior.

As far as how they conceived of their territory, it was a mix of both land and peoples. Pliny the Elder, for example, gives rough bordeers for Spain then further describes the territory by listing all the peoples and cities within it. Rome was an urban empire and they strove to make their subjects urban, so it makes sense that they made sense of their territory in that way. Of course, those cities and peoples had geographic borders too.

Romans tried to make the world into straight lines. Caesar described Britain as a triangle for example. This is scene best in their itineraries and sailing records. Basically, a journey was a trip between two points on a line, usually cities. The Mediterranean was a circle of these points. Italy would be a lot of lines leading from city to city. The best example of this is the Peutinger Table which is a medieval copy of a 4/5th century map. For more on Roman understandings of geography, check out Nocolet: Space Geography and Politics in the Early Roman Empire.

Probably not. It was an urban world linked by sea routes with a lot of raiding back and forth across the countryside. Hence Byzantine monasteries were built on mountainsides to protect the local farmers until imperial troops might arrive or the raiders just move on. When I was doing research for “Count No Man happy” and “Antonina” I came to realize how porous borders were. I think it is fair to compare it with the American West. There were Sklavian raids deep into the Peloponnese in the eighth century without any border change, and the impression I got from Theophanes Confessor is that they were nothing particularly unusual. Belisarius had to defeat a Bulgar raid on Constantinople only a few miles away from the city yet this relatively small bunch of Bulgar raiders would not have been able to hold the area. They moved on back home burning and looting on the way. The Persian frontier itself was pretty much settled with ancient fortified cities in depth yet Chosroes sent armies through Anatolia to just across the Bosphorus from Constantinople well knowing that he could not actually hold the area for very long or take the city itself. He could, however, demand cash to withdraw – which he himself needed to protect his eastern frontier against other enemies. He did the same in the Levant. It was all pretty fluid. One should also remember that the ancients did not think in terms of fixed frontiers as we do except as they constituted defenses. It is said that there is more Bulgar than Greek blood in modern Greeks yet there is nothing of Bulgar culture in modern Greece.

The Romans are the best example of this. They had a lot of limes which are basically fortified borders. Some examples are: Hadrian's Wall, Limes Germanicus (which separated Roman land from the german tribes), Limes Arabicus (the frontier of the Roman province of Arabia Petraea facing the desert).

Also let's not forget one of the biggest fortified borders of the world: The Great Wall of China.

I note you mentioned 'ancient' empires, and so you're not, of course, talking about empires like the British Empire or the Russian Empire, who very definitively thought in terms of territory and landmass (in fact, as an aside, there's a really cool map on the cover of a Niall Ferguson book called Empire showing the world with Britain at the center, with the Empire all around it, stretching over the North Pole etc. Fascinating!).

As for ancient empires, it's something of a mix. In the Roman Empire, the Roman conception of territory was an admixture of all three -- population centres, territory, and peoples. Taking Egypt, for example -- we know that the Romans thought of 'Aegyptus' as a land, with a specific people, built around specific centres of population, mostly the Nile delta. Their conception of Egypt certainly wouldn't have matched today's Egypt, and mostly the idea that a place like Egypt, surrounded by desolation on all sides, could have strict borders would be questionable to the Roman conception.

On the other hand, the Romans totally thought there were strict borders of their own empire -- take a look at Hadrian's Wall as a great example.

For the Romans, I would say that they largely thought of it in terms of conquering peoples, but there wasn't as sharp a distinction between people and territory as we might imagine. And of course geographic boundaries could be convenient zones of demarcation, although in practice they were more honored in the breach. The Roman army frequently moved beyond the limes and, as has been noted elsewhere in the thread, population could flow across the border in the form of people being settled within the Empire.

An interesting note is that social patterns overwhelmingly persisted from pre-Roman times along the frontier. My favorite example is that what frontier rebellions that occurred--eg Julius Civilis and the Batavians, Tacfarinas in North Africa, and Saturninus along the Danube--tended to lead by "Romanized" leaders with experience in the military but were built along alliances between local populations on both sides of the frontier. So when you think of these societies, it is best not to think of a thick black line separating inner and outer, but rather a zone in which the Roman army was but one of many forces acting upon social organization.

The main question I have from this, and it seems obvious, is:

Would it have been best to live far away from any borders?

It seems obvious, but would it? Maybe there were also advantages to living by borders, like for trading.

Your question touches on the fascinating subject of maps, their use and the techniques behind them, as well as the development of the idea of maps indicating territorial control and, ultimately, sovereignty. This is a (fairly) recent phenomenon and mostly associated with the "ptolemaian revolution“ in map-making. A cartographic revolution in the early renaissance transformed the medieval conception of space as either text-or time-bound to a “modern” version, where space was envisioned as grid-based, homogenous and divisible according to mathematical principles. In medieval times maps such as the „mappaemundi“ (literally maps of the world in latin) did not really indicate territory in the way we see it today. They (at least in Europe) were often essentially religious in nature (they would for example be hanging in churches) and would have Jerusalem at the center; There would be a rudimentary shape of the European subcontinent, but it would show just certain places of importance (other holy sites or destinations for pilgrimages for example). We would not consider them „accurate“, precisely because they do not follow the mathematical underpinnings that inform map-making today.

This social process of the transformation of maps and map-making can be understood as a historical assemblage of a variety of actors; re-discovered technical knowledge, mass-dissemination of maps through the printing press and the maps themselves, which produced new ways of spatial understanding. Here is the kicker: These new maps also helped replace older ideas of political rule as radiating from a centre to the periphery with new representations of authority as territorial. What does that mean? In medieval times, for example transfer of territory after a war would not be like we imagine it today; The document or treaty would essentially be a list of persons and places that would now owe allegiance to a new ruler (This abbey, that forest, that town etc etc). Rule was not defined through how large your territory was, but who you had authority over. This practice went on for quite a while, and maybe only with the congress of vienna in 1815 do we have the first „pure“ example of „modern“ conception and transfer of territory, based on a new understanding of the world and how to depict it. A point can be made that colonisation played a huge part; it was there that a „modern“ division of territory was first used and later "imported" back to Europe.

Source: Branch, Jordan. The Cartographic State: Maps, Territory and the Origins of Sovereignty. New York: Cambridge UP, 2013. Print.

How does this mesh with southeast Asia, Thailand, Burma, Laos...etc etc...where today it seems a border is more of a suggestion and people are very mobile? It seems that these nations have become more or less fixed states very recently, that territories would change hands regularly, and even capital cities would be moved/redesignated. How can I learn more about that geography?

I would say it depends entirely upon the level of hegemonic power of said ancient empire.

For example, the boundaries of the "Roman empire" were not thought of in terms of "state" boundaries like we have now, but in terms of the limits of "civilization" (with a slight connotation toward Mediterranean urban city civilization) itself. During the peak of the empire, almost any city of note in the Mediterranean or Europe was part of the empire, so by this logic, you could overlap the limits of civilization (the frontier limes) with the limits of the state, thus the boundaries would "kind of" represent what we think of as territory of control.

However, once the Roman Empire broke down to be subsumed by barbarian kingdoms, this view of the exact territoriality broke down as well. Because you had issues where for example, the Roman Empire having never given up its claims of ownership, was "internationally" recognized as such, but did not have de facto control (Ostrogothic kingdom of Italy comes to mind).

Not to mention the bigger problem of continuing overlap of kingdoms as representatives of ethnic barbarian entities under a different system from those of/under roman "ethnicity"/legality. Meaning that to Italian minds living under the Ostrogoths, it could be entirely possible to see the Roman Empire as not gone, and Theodoric (the Ostrogothic King) as merely being King of those of the Ostrogothic "nation" only, while simultaneously being the military governor for the Roman "citizens" under the Roman Empire in Italy. The difficulties begin when power shifts more firmly toward one end of this bipolar framework of leadership. What happens if the Roman Empire wants to claim more de facto control of its "military governor", what happens if the Ostrogothic king wants to claim more de jure control of his "kingdom?"

This doesn't even get into the concept of what constitutes nominal recognition of power. At what point is submission to a higher authority actually real, or just lip service? Then you get into more complicated debates over the question of what constitutes actual power and suzerainty.

Btw, you can see this in microcosm in the situation with modern disputed states. There are overlapping issues of claimed territory, de facto control, and international recognition. Only with all three recognized is there anything close to an actual "exact" border. When any of the three are disputed, it becomes a grey area. It's true now, it was true back then.

Long story short, yes, those maps showing exact territory are misleading. They are most accurate when an empire has the overlap of claim, de facto control, and recognition, least accurate when any one of the three is disputed.