By nature Humans want to take as much as they can to survive, thrive and propagate. You only need enough reason to convince others around you that you have the right to take it without them all teaming up against you and taking back your new acquisitions and maybe everything you own.
Most answers here have good points but complicate the question. I believe that in the vast majority of civilizations and societies there was a general belief of right to property and the differences were in who had the right and for what reason(s). To take another persons property you only had to differentiate why one has that right and the other does not possess that right.
For example regarding 'western' powers you might say it was believed that God created the earth and it was given to man. There was usually a strict definition of a man in this context. At one time you had to be of noble blood. At another time you had to be a Christian. You might have had to be truly a man and not a savage, as at one time the savages were thought to be less than men. Part of the justification behind conquest of the Americas was because it was believed that the savages were not capable of being civilized even if they converted to Christianity. It was up to the settlers (aka conquerors) to be stewards to the savages and their descendants, which makes sense if the race they belong to can never be educated to the level of 'true' men.
It was also taken into consideration that you were not an 'upstanding' citizen, maybe if you commit certain crimes against the people or the state, then you forfeit your right to property.
In the end it is always a statement:
We need more property
and an assertion:
We can take that property because current holders don't have a right based on ________________ reason. Fill in the blank and get it approved by an authority like a king or pope (Which usually only happens with general support of the people).
Examples I have read about:
Might makes right / survival of the fittest / right of conquest because God will ensure that the right side wins.
Heathens do not have the right of property and allowing them to thrive in their own lands is a threat to us, our lands and an insult to God. If we don't do our duty onto God and destroy the heathens then we will go to hell. Once they are destroyed it makes sense that God is rewarding the conquerors with said property.
This land belonged to our ancestors 2000 years ago and we are taking it back.
The people are savage and need us to take care of them and as they are like children they do not have the right to property.
The vast majority of the land is empty and not used. I have heard this is an argument used by politicians and people in power in reference to the Americas and Palestine. Combine that argument with some of the above and you may feel justified.