Kelly, AB9RF has a nice article, written in response to the question "Why the Hell Would You Want a Ham Radio?" It's a very good question, and one what we as hams I think don't do a very good job answering. Her answer is excellent, and well worth reading. Here is my somewhat shorter take on the subject.
When someone asks you "why the hell would you want a ham radio?", there is really only one way to respond: "why the heck do you want anything that you have?" Why bother submitting some one else's desires to some kind of scrutiny that you aren't willing to apply to yourself? Each of us has a great number of desires that we can't justify in purely pragmatic terms, and I think it is silly for us to try. Accept that a great deal of what we do is to satisfy our own personal desires, and that we don't have to and shouldn't try and more importantly shouldn't expect others to justify them.
If you ask the slightly different question, such as "Why would the average person want a ham radio?" the question has a somewhat different but related answer. It's far from clear to me that the term "average person" has any meaning in this context. There probably isn't even such a thing as an "average ham", since hams encompass such a wide variety of interests and practices. I like the idea of homebrewing, QRP, digital modes and satellites. Contesting and EMCOMM bore me to death.
I think when you are asked these questions, the best that you can do is answer why you personally enjoy ham radio. If it's contesting or EMCOMM that floats your boat, then you are the right person to talk about that aspect of the hobby. For me, it's the odd combination of building and using equipment which manipulates a fairly mysterious part of our physical world: the EM spectrum. I find the idea that someone in the U.S. could emit a signal with the power of 50 microwatts that could be detected in Australia to be absolutely amazing. That's what keeps me interested.