I just read Matthew 7. This has a bunch of the most well known passages in the bible. I think even most non-Christians raised in the Western tradition are familiar with most of these.
"Judge not, lest ye be judged, for by the judgement you pronounce, you will be judged"
"Do not cast your pearls before swine"
"Ask, and it shall be given. Seek, and ye shall find. Knock, and the door shall be opened."
"Whatever you wish that others would do to you, do also to them"
"Wide is the gate that leads to destruction, and narrow is the gate that leads to life."
"Beware of false prophets, who come to you in sheep's clothing but inwardly are ravenous wolves. You will recognize them by their fruits"
“Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven. On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’ And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’"
"Build your house on the rock, not on the sand". Words to live by!