I agree with paramedicpete that being a volunteer does not necessarily mean that people don't value your services. Often, the people you're serving may simply not be able to afford to pay a salary to everyone involved.
Having said that, I do have a problem with organisations that are turning a handsome profit on their activities, but use volunteers because they're too cheap to pay for the service. (For example, I volunteered at a "Western Days" county fair east of Calgary last summer. They were attracting huge crowds, and I'm pretty sure they were making money hand over fist; but I spent 12-14 hours there volunteering and they made us pay for our own lunch.) But I think what goes around, comes around; organisations that don't appreciate the work their volunteers put in end up finding it difficult, or impossible, to attract those volunteers. It's the volunteer organisations that treat you like a valued guest, rather than an unpaid employee, that get people wanting to participate. Personally, I'm never going back there.
As polak187 has pointed out, there are volunteer positions with some police departments, but I don't think you'll ever see a wholly volunteer police department. The problem is that police have a lot of power, and some might well volunteer for the wrong reasons or let it go to their heads. Whereas, very few people volunteer as a firefighter because they wanna bust heads...
A friend of mine, who used to run her own catering company, has been volunteering with her church, that has a large soup kitchen program. The minister in charge dearly wants the soup kitchen to be entirely run by volunteers. My friend has tried, so far in vain, to convince the minister that this is simply impossible. Volunteers may mean well, but soup kitchens have to meet the same health code as any other restaurant, and without a professionally trained restaurant manager (food services manager, whatever you want to call them) they could end up being shut down by the city, or worse. (Being a charitable organisation does not make you exempt from lawsuits, as the Roman Catholic Church and the Canadian Red Cross have found out.)
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"The mind is not a vessel to be filled but a fire to be kindled."
-Plutarch