Getting Biblical in Daily Life
Jewish Perspective
According to the Talmud—and this is going to be pretty surprising for Christian readers and interpreters—Daniel was not a prophet. Yeah sure, Daniel had visions and so did prophets like Isaiah and Ezekiel. But apparently a vision does not a prophet make. According to some Orthodox Jews, Daniel's inspiration was of a slightly lower order than that of the major and minor prophets. He received "divine inspiration" in the form of visions, but that's different from "prophecy" per se. (This distinction is explained in great detail on the Chabad website.)
Also, many Orthodox Jews—like the members of Chabad—wouldn't agree with the academic assertion (though we do) that Daniel was probably written after the events it seems to prophesy or predict. For instance, they would tend to believe that Daniel really did foresee the rise of Alexander the Great, whereas the academic consensus is that the writer of Daniel lived after Alexander (since he uses some Greek vocabulary and his language generally dates to that period).
Of course, that's a matter of faith, so no one's here to actively dispute it (even if we're not arguing in favor of it). Maybe the angels felt like teaching Daniel some Greek at some point (or something). (The relevant Chabad argument on this point can be found here.)
On the other hand, Liberal, Reform, and Reconstructionist Jews would generally accept the academic view of Daniel as a book representing the views not of the historical Daniel but of those living under the Greek Seleucids, seeking a way to retain their own traditions under rather hostile foreign rulers and looking to the example of Daniel to do so.
Christian Perspective
The Christian perspective on Daniel remains broadly similar throughout the different denominations. They're all pretty united in seeing Daniel as pointing towards the birth of Jesus and the incarnation of God. It was easy for Christians to look back at Daniel and see its depiction as being predictions of the incarnation of Jesus, what with the end of the Four Empires, the advent of a Messianic Age, and its description of "one like a human" who appears before God and receives dominion over all.
Eastern Orthodox Christianity sees the stone that destroys the scary statue in Nebuchadnezzar's dream as being a metaphor for Christ, as do pretty much all the other Christian denominations. But Eastern Orthodox Christianity adds in another bit, saying that the fact that the stone was "not carved by human hands" foreshadows the virgin birth, since Jesus won't be conceived by human agency, but by the power of the Spirit. (source)
Also, Christians view Daniel as being a prophet, not just a visionary seer (unlike in Orthodox Judaism). So, he ranks right up there with Isaiah, Jeremiah, Ezekiel, and the rest. Plenty of Christians see Daniel's prophecies as relating to future history. It doesn't just apply to the Four Empires and the arrival of Christ, but also to things to come. John Calvin is a notable exception. He differed from them in seeing Daniel's prophecies as only being relevant to the times leading up to and culminating in the life of Jesus.
Islamic Perspective
The Islamic perspective on Daniel—or in Arabic "Daniyal"—isn't all that startlingly different from the other perspectives. Like Christians, Muslims generally think of Daniel as being a prophet. He lives at the courts of foreign kings and instructs them with wisdom and helps them to serve God—in this case, by teaching them the fundamentals of Islam.
Aside from re-telling the story to show Daniel as a righteous Muslim instead of a Jew, Islamic tradition also contributes a new story, one bringing together the two major prophets Jeremiah and Daniel. Jeremiah is magically transported to a pit where Daniel has been trapped with two lions (in this version of the story, by Nebuchadnezzar). Jeremiah brings Daniel a hot dinner and they have a nice chat. It's sort of like the Abrahamic religions version of bringing Batman and Superman together in one comic.
(Or, maybe Batman and Superman would be more like bringing Jesus and Moses or Muhammad and Moses together in one story. So, bringing together Jeremiah and Daniel would be more like bringing together, say, The Green Lantern and Daredevil. Just to be technical.)
Baha'i Perspective
Members of the Baha'i Faith see Daniel as being a prophet. The guardians of the faith—interpreters like the son of Bahaullah, Abdul Baha, and Shoghi Effendi—have all worked with and interpreted prophecies stemming from the Book of Daniel, regarding things like the coming of world peace on earth. For example, the Manifestation of God who came before Bahaullah—the Bab—is said to have fulfilled the prophecy about peace coming after a 1260 day period in Daniel. (For more reading on this, you can go here.)