Getting Biblical in Daily Life
Jewish Perspective
2 Kings is obviously pretty important to the Jewish people—given that it's talking about the Jewish people, and was written by Jewish people, and implicitly gives advice to the Jewish people. The book is a reminder of how God gets involved in Jewish history and of how that historical relationship can take a particularly gnarly turn, given that the book ends with everyone getting sent into exile.
2 Kings tries to show sterling examples of people who are doing its version of Judaism correctly (a fairly strict Deuteronomy-based kind of Judaism). The best examples in 2 Kings need to be the prophets—Elisha, Elijah, Isaiah, Huldah—but also the good kings, like Hezekiah, Josiah, and Joash of Judah. These kings become models of Jewish behavior. They know how to observe the basic practices of Israelite religion, steering away from all image-worship and foreign gods. Josiah even manages to bring back one of the major Jewish traditions, Passover, which had been forgotten—and which, of course, survives to this day.
This website from the Hasidic Jewish organization, Chabad, provides some tales from outside the Bible related to Elijah and Elisha. In particular, it discusses how they first met—a cool origin story, like Batman and Robin getting together for the first time.
Elisha had a full head of hair back then, for one thing—unlike when those kids made fun of him for being bald in 2 Kings 2. He doubts his ability to study the Torah. He's like a "precious stone" that Elijah needs to polish and prepare for his prophetic mission. It's an intriguing back-story for these major prophetic heroes.
Catholic and Protestant Perspective
When Catholics and Protestants both read the Hebrew Bible, they tend to look for evidence of Christ—any hint, foreshadow, or prophecy that seems to point toward Christ is valuable. Take for example the extremely important Catholic theologian, St. Augustine. (He's really the Andre the Giant of Catholic Theology—unless that's St. Thomas Aquinas. At any rate, they both have a posse.) He interprets the whole of the Books of Kings as pointing towards the coming of Christ in The City of God.
The Gospels themselves have an important relation to the tales of Elijah and Elisha. Most obviously, Jesus does the same sorts of miracles that Elijah and Elisha do: multiplying food, curing sickness, and raising the dead. Jesus brings Lazarus back from the dead at the request of his sisters, just as Elisha brings the Shunnamite woman's son back from the dead at her request.
Christians also believe John the Baptist to be a return of Elijah (in a metaphorical sense, or even a literal one at times), since the Gospels point towards this idea (though the Gospel of John seems to contradict the literal sense). In the Christian view, Elijah eventually comes back from heaven after his flight on the chariot of fire in 2 Kings 2.
Sometimes, Christians have felt the need to interpret certain events from 2 Kings in a more allegorical light. For instance, Jesus says in John 3:13 that only he, Christ, has ascended to heaven—yet, in 2 Kings, we actually see Elijah ascend directly into heaven. So, that's something Christian theologians wrestle with, either reading Elijah's ascent allegorically, or interpreting Jesus' saying in a more metaphorical way.
Islamic Perspective
Islam typically accepts all the prophets and holy men mentioned in the Jewish and Christian scriptures. So it should come as no surprise that Elijah and Elisha are also endorsed as prophets and spiritual heroes in the Islamic scripture as well.
Elisha gets a few shout-outs in the Quran; he's definitely no stranger to the Islamic tradition. Along with a couple other great Jewish figures, the Quran mentions Elisha in Sura 38:48: "And commemorate Ishmael, Elisha, and Ezekiel: Each of them was of the Company of the Good." (He receives another, very similar reference in Sura 6:86-87.)
Bahai Perspective
In keeping with its tradition of seeing truth in all the world's major religions, the Bahai faith finds particular importance in the figure of Elijah.
In Christianity, Elijah returns after his flight into heaven by becoming John the Baptist. In the Bahai Faith, he returns again—this time, as The Bab, the leader of a spiritual movement that preceded the Bahai Faith and its own founder, Bahaullah. The Bab helps foretell the coming of Bahaullah, and lays the groundwork for the revelation of the later faith—just as John the Baptist had done for Jesus.
Latter Day Saints Perspective
The founding prophet of the Latter Day Saints (commonly known as Mormons), Joseph Smith claimed that Elijah appeared to him and one of his followers, Oliver Cowdery, while they were praying. Smith's vision of Elijah is described in terms reminiscent of the vision of Jesus at the beginning of the Book of Revelation and Daniel's vision of God as "The Ancient of Days." The vision reveals that Smith apparently considered "Elias" and Elijah to be different prophets, though most other Christians and Jews interpret them as being the same person.
Smith writes:
After this vision had closed, another great and glorious vision burst upon us; for Elijah the prophet, who was taken to heaven without tasting death, stood before us, and said: Behold, the time has fully come, which was spoken of by the mouth of Malachi—testifying that he [Elijah] should be sent, before the great and dreadful day of the Lord come.
(See this website for Smith's full written account.)
Jehovah's Witnesses Perspective
The Jehovah's Witnesses have historically taken an important idea from their interpretation of 2 Kings. Witnesses believe that, according to the Book of Revelation, only 144,000 Witnesses can live in heaven with God—but there are a lot more than 144,000 Witnesses in the world today. In fact, there are around eight million.
That's where the 2 Kings interpretation comes in. The way Jehovah's Witnesses interpret it, the character Jonadab (Jehonadab), who helps Jehu defeat Ahab's family, symbolizes a specific class of Jehovah's Witnesses who won't reign in heaven with God and Jesus as one of 144,000– but they'll continue to live forever in a perfected "Paradise Earth." The term "Jonadab" isn't used so much by Witnesses anymore—but the basic idea is still present. (See The A to Z of Jehovah's Witnesses by George D. Chryssides.)