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The galaxy is vast. Even in 10,000 years the Imperium is still in reality a patchwork of systems and alongside major threats like Orks, the spaces in between are often inhabited by minor xenos races. However how common do you think are human worlds/systems/pocket empires that have evaded Imperial or Chaos attention for any number of reasons?

Minor xenos races even if discovered by the Imperium may survive for the time being simply because they are of little importance and threat (ie Stone Age Tau), they are able to evade (Hrud) or on certain rare occassions are able to repel what limited forces Holy Terra is willing to throw at them. However human worlds are of prime importance to the Imperium from the Great Crusade up to the present. So non-Imperial human worlds will probably only realistically avoid attention by being inaccessible due to warp storms/poor warp lanes/something bigger blocking the way.

There's also the Ruinous Powers, without the psychic might of the God-Emperor to keep them in line, I imagine some 'free' human planets may have fallen to Chaos. However others may have marshalled their physkic resources and provide some protection from the Warp.

Given these things, how common do you think free human entities are in the galaxy? Does its simple vastness mean there's probably loads, or do ten millennia of utter horror mean the number will have been whittled down drastically?

Before he Horus Heresy, Horus and the Primarchs were ordered to bring humanity together under the Emperor. Now the Heresy stopped that short, but I believe afterwards the loyalists killed traitors and tried to bring the lost human colonies back into compliance.

As far as human planets, there have to be a lot of those that are either too primitive to join the Imperium. Even if the Imperials dropped down it might be too much effort to uplift them. But could be turned into a recruitment world for Space Marines. There is the idea that they have to save the savages who don’t know of the Emperor. In one story there are these crawlers that drive across a planet where they put drive the sea(I think it’s part of the Tyranid box set Fluff from 7th). They didn’t know much about the Imperium, but Adeptus Sororitus dripped down to bring them into compliance.

System spanning human empires probably have been mostly dealt with. Many of those seemed to be discovered and destroyed during the Crusades.

Now, don't quote me on this, since it's one of those weird snippets of 40k trivia that I got crammed in my head., but only about 1-in-5 of all the human worlds are part of the imperium.

I could be wrong, dunno, can't remember where I read that bit, but the 40k galaxy is supposed to be our galaxy and as such it should have at least 100 billion planets. So the million worlds of the Imperium make up about 0,1% of the galaxy. That leaves a LOT of room for everything else.

Remember that the Imperium of man is not a nation state, you can't just draw a few lines on the map of the galaxy and say "There, that's Imperium". Imperium is more like a bunch of far off island nations organised like Nato.
Only thing that really connects it together is a vague shared similarity in faith and technology. The line between what's Imperium or not could be quite blurry in many places. Places that never get mentioned because they don't have big important people doing big important things.

Thing is, if it doesn't have a model to sell to little timmy geedubs can't be bothered to spare a thought for it. This tends to skewer peoples preception of the geopolitical realities of the galaxy. You know, that most of the galaxy is just a bunch of ruins where Spessmuhreens of the glorious Dankmaster chapter battle the heinous Ebay KHAAIOSmuhreens over random spots on the battlefield and some nonsensical objectives that keep appearing without any rhyme or reason.

I suspect there are a lot of Non Imperial human worlds. The galaxy is a very vast place and humanity used to be all over it due to its golden age. But as you say, worlds encountered by either the Imperium, Chaos, or most of the Xenos races, likely don't remain independent human worlds long. They either become subjugated by one, or wiped out.

Don't forget that the Imperial Bureaucracy is inefficient and labyrinthine on a good day. There's certainly many planets that the Imperium colonized, conquered, or catalogued that have since been utterly forgotten by their nominal masters, and have since been left to their own devices.

The galaxy is a dangerous place, though. The Imperium couldn't exist if it wasn't. Any planet without recourse to a greater power for protection is going to have a rough time of it. Admittedly not so different from many planets that ARE in the Imperium... but at least when your planet is devastated by xenos, you're promised eventual righteous retribution.

You also have people living in things like space stations who can slip through the net pretty easily.

Some planets that get cut off do alright by themselves. They just need to stay loyal to the Imperium so when they get reunited they keep doing alright.

I also expect a lot of worlds in the Dark Imperium who have yet to be reached by the larger Imperium to be effectively "non-imperium" either by choice or circumstance.

The Imperium was made intentionally vast so that you could have any flavour of planet you can imagine.

I think it's totally possible to have some worlds that are cut off from the imperium especially after the Great rift. If they're lucky they are in an uninteresting part of the galaxy and left alone.

But if you're asking for worlds that are untouched by the imperium or Chaos but still around longer than 10K years? I think that's highly unlikely. The Great crusade conquered most human worlds I'd think and 10000 years are a long time to be found by some Chaos warband after the heresy, or some Dark Eldar raiders, or some Ork Waaagh. There might be some rogue trader stations, or even some rebellious planets that don't belong to the imperium anymore, but totally independent worlds should have been eaten by Chaos or Xenos up until now.

Don't forget that the Imperium also scrubs its histories of anything potentially embarrassing or anything that shows the Imperium in a less than positive light. When it loses sectors, it classifies the lost sector as wilderness space again, as they did with the Orpheus and Jericho Sectors (respectively from FW and FFG). It likely also redacts the public histories to avoid having to admit large scale defeat and losing territory.

"Orpheus Sector? What Orpheus Sector? There has never been such a sector."

A few generations of such purging and the only memory of such sectors would be in the garbled tales passed down from those that once traveled to or otherwise had knowledge of these now vanished sectors. A few more generations and maybe even those tales would have gone.

Similar purging could occur if any successful human rebellion defeats the Imperial response. In theory the Imperium might say they will return someday, but in practice they may cordon off the area and wipe it off maps and histories. Can't have people knowing about examples of successfully throwing off the yoke of Imperial oppression.

The Imperium provides safety and security and asks only for a fair tax in return. Those calling it tyrannical are heretics who seek to destroy the light of the God Emperor.

May the Emperor watch over you citizens.

I think there are plenty of world that are fully in and plenty that are fully out but I also think there would also be many grey areas. It partially depends upon what you take being in the Imperium to be. There could be:

Worlds whose ruling elite align with the Imperium but the population follow another ideology.
Worlds where the ruling elites are not aligned to the Imperium, so it is not in, but citizens volunteer to join the Imperial Guard, hence tithes are paid.
Worlds where there is imperial prescence like preacher and institutions, but the rulers and population do not align with the Imperium.
Worlds where some nations are in the Imperium and some nations are not.
Worlds who are not in the Imperium but the inquisition secretly run the show behind the scenes, fooling potentially even the plantary govenor, so they are effectively in the Imperium in all but name.
Worlds who are not in the Imperium but pay tithes to avoid becoming part of the Imperium.
Worlds who are not in but send forces to join the Imperial Guard to fight against a threatening alien race whom the Imperium are also at war with.

A non-Imperium aligned planet, without the protection of the Guard and no hope of reinforcement from anyone, is pretty much toast as soon as the first ork, 'nid, Tau, demon sets foot on it; I would imagine. Even many worlds with large sector wide assistance have trouble fending off such attacks, a planet going it alone is really going to have a tough time of it.

Any that survive a long time probably would have done so by sheer luck, being surrounded by warp storms or similar.