Getting Biblical in Daily Life
Civil Disobedience
One of the main things that Daniel and his friends do is defy the laws created by human beings in order to obey a higher law: God's law. Martin Luther King Jr. recognized this and gave the defiant trio of Shadrach, Meshach, and Abednego a shout-out in his famous, "Letter from Birmingham Jail," defending his resistance to segregation: "Of course, there is nothing new about this kind of civil disobedience. It was evidenced sublimely in the refusal of Shadrach, Meshach and Abednego to obey the laws of Nebuchadnezzar, on the ground that a higher moral law was at stake."
And there have been other instances of inspired disobedience, too. For example, Jehovah's Witnesses refuse to say the "Pledge of Allegiance" because they believe that their only real allegiance can be to the Kingdom of God, and not to any earthly kingdom. In 1940 the Supreme Court said that they could be forced to say it, but in 1943 it overturned its earlier ruling, defending their right to opt-out.
Today, civil disobedience on religious or moral grounds is still a very hot issue. You can see it playing out around the world. Very recently, the Chinese Government stated that it wouldn't let a single word said by the Dalai Lama—the spiritual leader of Tibetan Buddhism—out onto the airwaves or even onto the internet in China, condemning him for "reactionary propaganda." Of course, Tibetan Buddhism is obviously a different religion from the Judaism of Daniel, but you can see the same kinds of courage and principles at play.
The End of the World
This is really more the Book of Revelation's wheel-house, but people who believe the world is about to end also look to Daniel to try to find prophecies that seem to point towards things that are happening today. A simple Google search for "book of daniel end times" should yield a plentitude of results, with numerous sites all arguing to connect up present day events with visions from the ancient book.
Daniel has plenty of visionary images that people continually re-interpret in terms of the situations they find themselves in. Instead of seeing the four beasts as representing Babylon, the Medes, Persia, and the Greeks, someone might claim that one of the beasts represents the Soviet Union or the European Union or the UN—or whatever somehow happens to seem like a good fit.
Religious Persecution and Tolerance
This is a huge issue today. Whether it's the Chinese Government persecuting Tibetan Buddhists, or Buddhists in Myanmar persecuting Muslims, or Muslims in Egypt persecuting Christians, or Neo-Fascists in Hungary and Greece attacking Jews and Gypsies, there's some horrific act of religious persecution going on in the world at any given time. Going back to earlier times, we see the same awful events playing out: Christians getting thrown to the Lions by the Romans (and unlike in Daniel's story, getting decidedly eaten), Jews and "heretics" being tortured and executed by the Christian Inquisition, and the persecution of groups as various as the Quakers and the Mormons.
Daniel, in a way, provides a textbook for what to do in these situations. And it basically says, "Stick to your guns." It shows Daniel and Shadrach and friends surviving brushes with death in order to come out on top in the end. Still, the Book knows that few people are going to be lucky enough to escape a more grisly fate. It says that the tyrannical Greek King, Antiochus IV Epiphanes, will be able to get away with his persecutions for a set time and will successfully martyr many wise and holy people.
But at the same time it suggests that those people will also escape from the "fiery furnace" or "lions' den" they're stuck in. They'll be resurrected from the dead and will receive their right rewards at the end of time. This is another way of encouraging people to act on their convictions. You shouldn't be afraid to, because you know things will ultimately turn out right in the end (even if you have to come back from the dead for that to happen).