Jews consider Psalms an essential part of the worship cycle. When someone Jewish dies, many religiously observant loved ones will continue reading Psalms aloud next to the body until the person is buried (source). This way, the body is never left out of the presence of either man or God. Nifty, right? This custom highlights the poetic nature of Psalms—in death, the person's spirit is read poetry and music, not stories or laws. We mean, come on, no one even wants to hear ancient tax code while they're alive.
Although different sects of Jews differ on their use of the book, almost all Jewish prayer books (called Siddurim) contain large portions of the Psalms (source). Because of their musical nature, they work well for mass readings and services that praise God and ask basic questions about the nature of faith. Again—imagine reading out rules and regulations at a concert...not the most rousing experience.
Psalms is a book about faith in the face of opposition, and its original use as a community-builder continues to this day.
Psalms may not be an integral part of Muslim liturgy, but it belongs to a tradition that Islam considers vital to the Qur'an's heritage: according to Islam tradition, Psalms was transmitted to David in the same way that Mohammed was given the Quran (source). That's right—divine inspiration at its height.
First, let's make it clear that Jesus loved him some Psalms. Check out the Gospels—say, Mark—for some proof. He quotes them like it's his job. Which is just may be.
Psalms has also been an integral piece of Protestant worship for centuries. After the Reformation, many psalms became hymns sung in Protestant churches. Psalms speaks to the individual's struggle to find faith in a hostile world—you can imagine how this motif spoke to many Protestants throughout the period of the Reformation in Europe. At its best, Psalms could be pretty comforting.
In the 17th century, when the Pilgrims arrived in the New World, one of the first books they printed was the Bay Psalm Book, an English version of Psalms set to meter—Harry Potter wasn't out yet. Psalms is also read fairly often in Protestant tradition in conjunction with Proverbs.
Catholics aren't kidding around about the Psalms. Here are just a few fun facts about how they're used: