Whenever the phrase "We have conquered the known galaxy" is used -- sometimes by a politician, almost always by a demagogue -- it must be considered hyperbole. The known galaxy, after all, is much larger than the part of the galaxy that has actually been settled by the sentient races, and as knowledge has a tendency to increase faster than civilisation has a tendency to expand, conquering the known galaxy is, according to many, a virtual impossibility. Those who insist on using the phrase "we have conquered the known galaxy" as if it were immutable fact are usually suffering from delusions that make other aspects of their life difficult.
It is far more accurate to say "most areas of space where sentient life has settled and established itself are quite thoroughly conquered." After the discovery of superluminal travel, the races leapt from habitable system to habitable system, settling on the viable worlds and trying to make what use they can of the rest. Centuries of this has resulted in hundreds of thousands of planets that have been thoroughly settled and tamed by two score intelligent races, all living together in various combinations of harmony and discontent.
But even that phrase, however much more accurate it might be, is too forceful if put in its proper perspective: Although hundreds of thousands of planets have been settled by sentient races, that number is hardly worth noting when compared to the projected number of habitable worlds in the galaxy. We have to date settled no more than an eighth of a hundredth of a percent of what Terrans call "the Milky Way," which amounts to little more than the tiniest fraction of one spiral arm.
But from another perspective -- the finite perspective of the sentient races that have carved out a niche in a vast sea of stars -- the populated portion of the universe is, as some might say, "plenty large."
The Alliance of Free Worlds, a relatively benign Interstellar Republic, is comprised of more than 75,000 habitable star systems. The Empire of the Radiant Throne, a somewhat less benign theocracy, claims more than 50,000 worlds in the name of the Divine Emperor Elana Torvoo XII. There are half again as many systems claimed by other, smaller interstellar powers, the most notable being the Free Trade Baronies, and then tens of thousands of independent systems, frontier worlds, and inhabited worlds that have been overlooked and forgotten by civilised society...
Taken from An Informal Guide to Known Space, Edition XVI, McPherson/Sovitt Publications.