I recently read an article titled How to Do Philosophy. As someone who majored in philosophy, I mostly agree with the writer, and shared a lot of the same frustrations in my studies. I'd say the material was half stuff that seemed to have practical application somewhere, and half stupid bullshit. The subject I usually cite as my prime example is epistemology. I am not sure if the wider field of epistemology is different from this, but we spent most of the semester arguing about whether you could have knowledge of the outside world. If you come to the conclusion that when everyone in the world says that they "know" something, when they don't really know it, something has gone wrong. Yes, it's true, I do not know whether I am a brain in a vat who is part of an experiment being conducted by a mad scientist. But I know that the Dow Jones is over 10,000, and I know that George Washington never studied kung fu at a Chinese monastery. (Or did he?) Only an asshole would tell me, "Well, you don't know that you're not in the Matrix, so you don't really know those things."
The parts of philosophy that I thought could be useful for something were, generally speaking, things that could feed into the field of ethics, and most people would agree that ethics is a worthwhile field of study. For example, there is a branch of metaphysics that is all about causality. How do you determine what and who played a causal role in an event? And how responsible can you hold someone for failing to prevent something? The answers to those questions can be really important, and it often takes a philosopher to give a satisfactory answer to them.
A few years ago, I took a philosophy class at Portland State, and though I was not at all impressed with the professor, he did articulate what I think is the best definition of what philosophy is: the study of the construction and evaluation of arguments. Regardless of whether any person agrees on whether that is what philosophy is, one cannot doubt that this is what one is doing when one is doing philosophy, and I believe that this is what makes philosophy a worthwhile study. A philosopher can make an argument like a ninja: define some terms, mention out some logical connections, throw down a conclusion. BOOM. Done correctly, one can only disagree with the conclusion by disagreeing with the definitions and premises.
The general problem with this, of course, is that people are rarely persuaded by logic. One needs some appeal to emotions and values in order to convince someone to change their opinion. But that's a story for another time. Some recommended reading on that subject would be Harry Frankfurt's "On Bullshit" (which can also be found in an anthology of his papers, titled "The Importance of What We Care About") and the anthology "Bullshit and Philosophy," edited by Gary L. Hardcastle and George A. Reisch. Seriously, if you read no other works of philosophy in your life, you should read these.