Seriously, though, I can think of at least a dozen good reasons to submit something to an unpaid market, and I'm sure your dozen will be different from mine. There isn't anything wrong with giving your work away, within a few parameters.
Don't send your piece to a nonpaying market first.
"But," I hear you say, "I'm a new author and I haven't had a lot of things (or anything) published yet. I should start with nonpaying markets for the experience." What you're telling me is that you don't think your writing is good enough to be paid for. If you really believe this, don't send that thing anywhere! Work on it some more, until it's as good as you can make it. Then follow the advice of editor extraordinaire Erin Evans: Start at the top. When you've made that story or poem into the best piece of work you can write, send it to Clarkesworld or Fantasy and Science Fiction or whatever is the most challenging market for your genre. Aim high. Give every piece the chance to succeed beyond your expectations. And when your manuscript comes back, turn it right around to the next most challenging market, and keep sending it out. Nonpaying markets are the publishers of last resort for your work, generally, not the first. Starting out at free is a way to never challenge yourself to be better.
Consider the alternatives to nonpaying markets.
Your story is good. It's really good, and you love it like a child, but no one wants to pay you to publish it. Now what? You have several choices: you can hang on to the story and resubmit it in a year, or two, or five. From my own experience, I know several successful authors who have recently found publishers for old, previously unpublished stories. Sometimes, it's not your story, it's the timing. If you wait, you might hit the right market at the right time, some other time. Don't like that idea? You could also self-publish. It's never been easier to self-publish ebooks, and the number of short stories and novellas for sale on Amazon puts the lie to the idea that you can only sell novels online. If you have a few pieces that have collected their share of rejection letters, why not bundle them together in your own anthology?
Not unpaid all the time.
There are all sorts of good reasons for deciding to submit to a nonpaying market. (Here are a few: The Value of Free.) But all of the arguments that go something like "If you were a house painter or a bus driver or an architect or a code monkey, would you work for free?" are at least partially true. Obviously, there are circumstances in which all of these professionals, and most others, would in fact work for free. But only rarely, and only in the larger context of being a paid professional. The time you spend on your work is as valuable as theirs, as is the product that you produce. Creative people too often sell their talents short with the excuse that "It's only a hobby" or "But it's not my real job." Bullshit. You can give away free samples for the same reasons all those people offer you little cups of goodies in Costco: to raise awareness of your product, so that people will come back and buy more.
Not all nonpaying markets are created equal.
You need to understand why you're giving away your work. Are you doing it to raise your professional profile with future publications, to make more readers aware of your work, to show your support for a publication or a cause, or to get a particular story to the audience most likely to enjoy it? Then consider what kind of nonpaying market is most likely to accomplish that. You may get as much traction out of a well-placed free sample on your own blog, website, or social network site as you would by allowing it to appear in a publication with a limited readership or one that's not particularly known for quality. How do you evaluate the relative merits of nonpaying markets? My best advice is to read about the publication in a place like Duotrope, google to see what other people have said about it, and then read the publisher's web page with a critical eye before you submit. Don't be taken in by places that want to charge you a reading or editing fee, that want you to purchase or sell subscriptions, or that have lengthy publishing histories and still don't pay their authors.
By all means, give away your work from time to time. Just keep in mind what you're trying to accomplish, and don't make a habit of it.