It seems in most novels that the Imperial guard and countless innocents are slaughtered by orcs, chaos, tyrranids and the like, yet the total population of humanity is never depleted.

This questions asks if humans are altered in some way, hinting that it might be why the Imperium of man is still going strong. Is this the case, or is some other factor at hand? Is this addressed in any of the books/games/other media?

How did the Imperium of Man become so well populated?

The Spread of the Imperium of Man

The real reason the Imperium of Man has spread so far (relatively speaking, the Imperium only covers one quarter of the entire galaxy even in the 41st century) is because of several millennia of expansion, once during their Fusion Age of barely faster than light expansion for 14,000 years and then another 10,000 years of faster than light travel when Humanity first learned to skim the surface of the extra-dimensional region called the Immaterium.

Using the Immaterium, Humanity was now able to travel much farther and more accurately than it had ever before. This brought about the Age of Technology, where new technologies and social transformations spread Humanity everywhere their ships could reach. During this time, humanity had even come into contact with alien races and established treaties of non-aggression. These would eventually be destroyed with the coming of the Age of Strife in the 26th Millennium.

During the Age of Strife, Mankind's hubris brought about the creation of new weapons of war and technological transformation and that war created machines which began to attack the worlds of the Imperium. At the same time psychic abilities turned from myth to fact and psykers started appearing everywhere. The Fall of the Eldar and the coming of the Chaos Demons also took place at this time. For the next 15,000 years, the Galaxy as we knew it began to unravel and the Golden Age of Humanity was undone.

Humans continued to travel faster and faster using Navigators, psykers who could navigate through the Immaterium better than previous ships, and this ensured mankind would continue spreading through the stars. However, as the Chaos Gods formed and the Eldar retreated from Imperial Space, the Immaterium became unstable and more difficult to travel through. This began to slow the expansion of the Imperium and eventually would limit it size due to the new hazards of travel through it.

For 5,000 years the Immaterium could no longer be effectively used for long distance travel due to corruption caused by time spent there. The longer you were in the Immaterium, the more likely you were to get lost and be unable to return to the material universe. During this time, the federation of worlds of the Imperium collapsed as daemonic possession, planetary corruption and the failure of the economic systems of the empire took hold.

In the 30th Millennium, the Fall of the Eldar is complete and the Chaos Gods tear from their gap in the Universe and begin their war on the galaxy at large. The Adeptus Astartes are created and the Immortal Emperor of Man join the battle against Chaos. Unfortunately, one of the greatest of the Emperor's soldier's rebels and helps to create the Chaos Legions.

The great struggle ends with the Emperor encased in a life-support chamber using his incredible psychic might to create a beacon through the Immaterium called the Astronomicon. This beacon is now what Navigators use to travel through the Warp and has restored the ability of the Imperium of Man to travel during its troubled times of endless war.

By the 41st Millennium, the Imperium is embattled on all sides, and its expansion stopped by Orcs, their merciless extragalactic enemy, the Tyrannids, fleeing, despondent and dangerous Eldar, awakening and undying Necrons, and allied occasionally by the Tau, a young, energetic, technologically talented race that still believes in a "greater good."

Map of the Imperium of Man
(Open in a new tab to see it in far greater detail)

See Also:

In Warhammer 40000 are normal humans enhanced in any way?

How did mankind travel through the warp during the Great Crusade?

Before the Fall of the Eldar the Hyperspace was less dangerous, the forces of Chaos were much weaker or nonexistent in real space. Humanity had practically no enemies. This "Age of Technology" lasted for many thousands of years, it was probably the time period where humanity colonized and populated much of the Galaxy.

Do the maths

(Good input from Fulli and Red_Shadow in the other answer):

Canon

(is it? official link please)

The Imperium of Man has tens of quadrillions of citizens scattered
across millions of worlds in the Empire.

Numbers

• Definition of a quadrillion in UK and AmE would be 10¹⁵, or 1,000,000,000,000,000.


• 
  Tens of quadrillions would simply be, let's be generous and have 90 of q. == 9 x 10¹⁶
  

Aside:

• Millions of worlds at, say 900 millions == 9 x 10⁸
  


• Makes 900 Million people per world on average, which is really not too much

Population maths

Using a reproduction rate of 1,1 (daughters per mother) and a generation duration of 35 years give or take, we get roughly 900 generations over a span a bit more than 30,000 years.

To get to the current population (based on the net reproduction rate only), we have to multiply the starting population x 1,1⁹⁰⁰.

• 1,1^900 =~ 1,8 x 10^37 (even with a base population of 1 (!))


• Let's some simplistic rounding and simply use 10^40 as the expected number


• If we were to use 20,000 years as reproduction timespan, we'd get something like 10^25

If we take "tens of quadrillions" to mean 10^17, then even with a reproduction rate of 1,1 per generation this means we're left with a factor of 10^8 (-> 25-17), that is 100 million times less humans than there could be.

In other words, to get at a population of 10^17 over (even only) 20,000 years, we have to use a net reproduction rate (with a generation span of 35 yrs) of 1.071: That means, per 100 women, you'll have 107 daughters, that is, only 7 out of hundred women would have more than one daughter.

So, if anything, the Imperium is thoroughly under-populated (as well as it should be given the setting.)

I think something most of you are forgetting is that the lifespan of the average human in the Imperium has increased significantly from the lifespan of current humans. Even regular, non-Space Marine humans regularly live for at least a century, sometimes longer depending on their station in life. Couple an increased lifespan with the fact that birth rates probably have not slowed at all and that can lead to a population explosion. Some worlds in the Imperium are also known for using cloning technology (Krieg comes to mind). Factor in all these things and the fact that this recipe for a population explosion has been going on for at least 20,000 to 30,000 years and it is not difficult to see how a single hive world can be home to literally trillions (that's right, trillions) of humans.

Although this is old, I still want to add my two-cents.

I think that, during colonization, the new colonies would likely have used technology to increase reproduction (more people born at a time, amongst other things, not grimdark). After all, they'd have a whole planet to fill and, in the early days, they were pretty much on their own. Safety in numbers.

This probably helped encourage humanity's rapid technological advancement, too. Within about five thousand years, humanity was close enough to the Eldar (during the Eldar's golden age) to be able to ignore the Eldar as a valid threat. They could even shoot blackholes through time. The Eldar, at this time, could re-arrange constellations for their own amusement. They were not a valid threat to humanity. Do the math. Humanity was a federation of planets at this point in time.

Hope this gives some perspective on humanity's rapid reproduction (necessity of having a whole planet to fill) and technological speed racing (the Eldar were basically Dark Eldar and were humanity's closest neighbors while human worlds were mostly cut-off from each other, good incentive to advance quickly, not to mention the threat of Orks and other things).

The Imperium is not soo well populated when you just use the Numbers.

If the population is 1.5 times the size of the last, and one generation is at least 80 years old you get in the year 40.000 the total of 5.250.000.000.000 citesence of the Imperium.

But keep in Mind that the Galaxy is a Dangerous place and many millions day per day.

By a total of a (estimated) million Worlds the Imperium holds you would only get 5 million per World. Thats the sice of a tiny Makropole... therfore many worlds must be less populated agra worlds to support the bigger ones we konw about. An Agrar world is fast builded, especaly when you ceep in mind that the adeptus mechanicus can still terraform whole continents in a coupple months.

For 40.000 years i think the Imperium isnt that well populated at all.