Who has been able to gain the services of an artist without pay? How'd you do it?
Understanding that this is a touchy subject for graphic designers/artists...
I think it has probably been said before here much better than I'll put it, but
there's always some type of "pay" involved 
Artists, like every other profession, will prefer the monetary ($$$) method of "payment", so they can eat and live, but there are times when artists/mechanics/restaurants/painters/webhosts/t-shirt sellers will accept another form of "payment".
You can't "expect" it of course, or ever feel like you're doing them "a favor", but it's possible that when the stars are aligned and the person has time that they might accept other methods of payment.
Always present it as an exchange, and not like you're doing them a favor by letting them design something for you, and you'll go much further.
With a friendship, the pay is a "favor between friends". You can get artwork that way by trading on your friendship if you have a friend or relative that knows how to do artwork. The exchange is that they feel like they are doing a favor for a friend/relative and you get the artwork. There may even be a loose promise of a monetary payment later on.
In a barter, the pay is a product or service that you can offer that is equal/greater/sometimes lesser value than the product service you are requesting. If you have a server, and the graphic artist needs hosting, you can offer hosting service for x number of years for a graphic design project. If you have a skill/service/product that you can offer, this is one of the best ways to get work done on a low budget. See this classifieds post for example:
http://www.t-shirtforums.com/showthread.php?t=6431
When a designer is "building up a portfolio", the payment for them is often still monetary. Sometimes they will accept "less" monetary payment when just starting out, and sometimes they will accept no monetary payment (maybe with certain copyright stipulations), but usually they will get something other than "experience" out of the exchange. Maybe it is a design that inspires them, maybe they have their own personal reasons, maybe your company
already has a high profile and it will give them
true exposure to have you among their client list (if you are just starting out, this is unlikely).
Sometimes you'll catch an
artist who is bored, or does it as a side hobby. The "payment" for the artist in this case is a cure for their boredom.
In a
non profit situation, the artist will sometimes "donate" their time in exchange for a tax writeoff, goodwill, good feeling. Sometimes the artist will still get a monetary payment, but just at a discount from their normal rates.
There are some designers/artists who create work in the spirit of an "opensource" or "public domain" license. You can see this on sites where they are offering
icons for free,
website templates for free, or other similar formats. Their payment comes by more name recognition/branding for their site, building of an email list, backlinks to their site, or for another related reason. Some of these works still retain copyright to their original artist.
There are some artists who don't know better or don't care. They may be young (in high school or jr high, but with great graphics skills). They may be living in a region where a smaller monetary payment goes a much longer way than where you might live, or they may take your word on "possible" exposure "down the line". Their payment might be the experience of doing another design, working for demanding clients, or hindsight experience when they learn what they've given away.
That being said, I have paid from $0-$1000+ for graphic design work.
Most of the times when it's been on the $0 end, it has been offered by the artist/designer. I don't feel comfortable approaching a designer asking for free work (I don't like accepting it either).
I think your best bet is to work out an equal barter of some type, I think that will get you the furthest.
