If you’re an artist, a musician, a website designer, a writer, than you’re used to getting requests to create something for people. And more likely than not, the requests come from people who don’t want to pay for said product. If you’re a pro-artist/musician/writer, odds are you’re just going to say no to these requests since that’s how you make your living and therefore the only exceptions can be the occasional support of a meaningful cause or a favor for a friend. If you’re not a pro, however, then being creative is not necessarily about money and odds are whoever’s asking you might have a better shot at getting something for nothing.
Do you guys see where this post is going? I’ve been drawing all my life and therefore I think the things I create are worth something. But on the other hand, I have a day job and illustrating is just something I do for fun other than the occasional commission. But most of the time, the requests I get from people to create something are for those who want it for free. To those who’ve made those requests and to others who hope to get stuff for free from people but don’t know how to approach the issue, I’m not saying you shouldn’t ask. However I do think it’s important to ask in a way that shows respect for a person’s time.
Example: Sometimes people want me to paint their portraits for blog headers or sidebars. No problem. I love doing that sort of thing. But unless it’s a commission, I have to pick and choose which ones I have the time to say yes to. 
Personally, I am way more likely to oblige someone if that person has supported me in some way, even if it’s in a small way like giving a shout-out to something going on on My Style Canvas on her own blog or Facebook page. (Example: The illustration here, of blogger DG Palmer of Dear Girl blog and Scopic magazine, was done upon request. I had no doubt about whether or not I’d say yes–since she’s always supported this blog by linking to my site on her homepage and leaving thoughtful comments.)
I’m just mentioning this because lately I’ve gotten more requests from people I’ve never heard of before–never said hello in the comments or via email–and aren’t offering anything in trade for my time. I admit it’s flattering to some degree to be thought of, but honestly I’ve never said yes to any of those people and that is not likely to change.

The point here is that the thing to keep in mind is that even though people enjoy being creative, doing something like writing a song or an article or designing a website or a dress or–ahem–an illustration is something that can take quite a bit of time and effort. And it’s important to acknowledge that much before requesting a freebie.

Another way to go about it could be a trade in services if you’re a crafty or artistic person yourself. Or if your site gets a lot of traffic, offer a link on the side of your page as payment, at least for a few months, the way you’d display an ad.

Another way of saying, there are ways to get what you want even if you can’t afford custom artwork. Sometimes it’s just a matter of being nice and making some sort of effort yourself.