Modern Judaism claims Israelite history as its own, so it's no surprise that Jews consider Exodus to be a foundational text of their faith. But it's not just about the stories and the nice, fluffy feelings of togetherness. Many specific regulations in Judaism come from interpretations of Exodus.
Examples? We've got plenty.
There are tons more where that came from. Go ahead and scour for yourself. We dare you.
A version of the Exodus story appears in the Qur'an, but it's pretty different than the one we read in the Hebrew Bible. Check it out for yourself to see where the differences are.
Moses is a pretty important guy for Muslims—they think of him as a prophet leading up to Mohammed. That means they interpret the themes of the Exodus story as indicative of the future coming of their prophet.
In fact, one of the recurring motifs of Exodus is the idea of the chosen leader, the man who is picked by God to do God's work. In Deuteronomy 18:15 (and remember, Deuteronomy is a retelling of Exodus), God says, "The Lord your God will raise up for you a prophet like me from among your own people; you shall heed such a prophet." Muslims believe that prophet is Mohammed.
Christians use the Hebrew Bible as part of their sacred scripture, so Exodus is front and center for them. Just like Muslims see the story as a forerunner of Mohammed, Christians see it as a forerunner of Jesus (source). Moses even makes his way into the New Testament. For example, in Acts 7:39-53, the writer explains the Jews' rejection of Jesus in the same terms as the Israelites' rejection of Moses in the creation of the golden calf. In many branches of Christianity, Moses is even considered a saint. And if nothing else, this has led to some really cool art. Michelangelo, anyone? (And yes, those are horns. That's a whole other story.)
It's not surprising that this story has been adopted by so many communities. After all, the struggle for freedom is a universally moving theme, don't you think?