A route of many roads leading from nowhere to nothing." —Ambrose Bierce
A few years after he wrote this definition in his Devil's Dictionary, Bierce wandered into the Mexican desert and was never seen again. Since consistency isn't a common trait among philosophers, he deserves some credit (though he wasn't really a philosopher himself). Jean-Paul Sartre, the apostle of French existentialism and its gospel of meaninglessness, found it impossible to live according to his own theories and eventually joined the Communist Party to feel like he was accomplishing something. Ernest Hemingway, a Nietzschean naturalist whose literary anti-heroes overcome every difficulty by strength and wit, shot himself in the head, unable to overcome his own depression. The list goes on of men whose ideas were defensible on paper but impossible to adhere to in actuality. Men like Bierce are something of an anomaly.
True philosophy is more like the Yellow Brick Road—there's only one correct route, but there are lots of false turns and forks that lead to fields of poppies and flying monkeys. Philosophers are even a lot like Dorothy—by engaging in the philosophical endeavor, they gain access to the goal (Truth), but most of them don't realize they're wearing magic slippers until they've gone the whole way on foot (if they even realize it then). It's not so much that philosophy goes nowhere, as that philosophers are easily distracted and often find themselves wandering into forests of grumpy apple-throwing trees. When they start pursuing something other than Truth, they've stopped being philosophers in the proper sense.
So if it's mostly just a series of wrong turns, why study the history of philosophy? To borrow from St. Thomas Aquinas (who borrowed from Aristotle), everything has precedent. Aquinas claimed the only entity without precedent (the "unmoved mover") was God, but that everything else was the result of something before it. For instance, I'm typing this article right now, but in order to do that I had to get up this morning, and in order to do that I had to go to sleep last night, and in order to do that I had to be alive. . . and so on and on. Everything becomes interconnected and can be seen as the result of something else, until we get to God who is the beginning of everything (and the end of everything).
The same holds true for ideas. The philosophies currently popular didn't just invent themselves, they were born out of past ideologies. Today Christians are confronted by the claims of relativism, postmodernism and nihilism, but past generations dealt with different issues. Postmodernism grew out of existentialism, which grew out of modernism, which grew out of Enlightenment rationalism, which grew out of Renaissance humanism, which grew out of medieval scholasticism, etc. (to put it very simplistically). We can't really understand postmodernism unless we understand the philosophies that came before it. This holds true of any philosopy.
The purpose of study isn't mere knowledge, of course. Our Christian worldview is the way to Truth, and we need to be grounded in our faith before we venture into the witches' castles of secularism. However, the proper response to pagan philosophies isn't to ignore them. We understand them to stand against them. The history of philosophy provides the context by which to achieve such understanding.