As a media coach, and former Presenter for Monster.com's Diversity Leadership Program for outgoing college students, I've been asked this question many times, and the answer is always the same: Definitely Maybe. 
Over the years I've been hit with many angry responses to my advice, ranging from 'You should never work for free!' to 'You'll only devalue yourself if you work for free' to my all-time favorite, 'But I have a college degree!' 
There are endless articles online, and in print, that will tell you that a college graduate is expected to make X-number of dollars in their first year. While that may be true for some industries, it is by no means the case across the board. For most of us, what employers really want to see, more than your fancy piece of paper (which I guarantee they don't really want to see!) is some value in you. Having studied something specific in university simply isn't enough, and that's a good thing. 
What are you made of? What are your work characteristics? Your productivity? The hidden talents that you don't even know you have? No one can know that just by one interview. They can, however, get an idea of how you tick by delving into your work history.
What's that you say? Just got out of college, and don't have a work history yet? A-ha- that's where volunteering comes in. Align yourself with a company when there is absolutely no risk to them. That's just good business. You have an opportunity to show them what you're all about, and they get to see if you're a good fit, without going through reams of employer paperwork. 
You may not be guaranteed a paying job for your final effort, but I'll bet you'll go home knowing more about your chosen industry than you did that morning. Plus, you'll be networking with others all day long in your field, and if your field is anything like mine, you will run into the same people over time.  
Here's a little secret. Start your job search before you graduate. Intern while you can under the credibility of your university. Trust me, this opportunity won't be as available to you later (which I'll go into at a later date). Attorneys do it. So do business students, and anyone else savvy enough to think about the fact that companies are inundated with resumes from recent college grads each year. And guess what? Many internships are non-paid. 
In my own industries: TV, radio, and entertainment, the competition is fierce, so any networking is a benefit. And if you're looking to break into showbiz and make a good living in the first few years? Yeah, well, good luck with that. 
So, yes, I am a big believer in volunteering your time, and effort fresh out of college. Arguably my career has been predicated on it.  Through volunteering, I've made friends, gotten well-paying jobs, and I sharpened by skills too.
All this being said, what I would caution you on is to limit your volunteer work. For every honest employer who wants to 'give back' to the next generation, there's some jerk ready to take advantage of your good nature. Never take a volunteer job without having some work strategy (like a limited time, or number of hours).
Just remember, quitting a volunteer job should be just like quitting a paid job. Unless there are dire circumstances, you should give notice, and act professionally. I've seen more than one intern out there who didn't think it mattered how they acted, since they weren't being paid, so they were reckless. They took office supplies; they came in late, they didn't give notice when they left. So how do you think we treated their resume when they tried to get a gig a few months later? 
In short, you should at least consider volunteering in some capacity that will help you, even it isn't monetarily. You never know where the road may lead.