I have seen the suggestion that when Washington's second term ended, it came as a surprise or was even seen as a selfless act that he walked away from power. How much of this is part of our own myth making and how much of is true? Did some Americans and Europeans expect that Washington would set himself up as all but a king for life, replacing one tyrant with another?
Washington would have seen how complicated--and dangerous--position as a "king-like" figure would be. He was involved in the Revolution--for independence from Britain and its king--and as president, would not have likely wanted to see a return to the same kind of structure. If it would have been relatively easy for him to be president indefinitely (or be "king"), it could have also been easy for someone else to do so in future. If you claim to be interested in the fate of your new nation, you'd not likely set a precedent that would see a return to any kind of situation where what you fought to eliminate would return.
He basically set the pattern for his office as he went. It's important to note that he was elected while the Constitution, Bill of Rights, etc, was being created. He actually pushed to have those things done; he knew the alternative would be anarchy.