If you're good with graphics software, you can create your own website logo.
But it is the sort of thing that's worth hiring out to a specialist once your site reaches a certain level of popularity (but before the masses arrive).
This page provides help for finding free, inexpensive DIY or custom website logos.
A quick Google search will bring up options for free logo creation. The ones that are truly free won't provide you with a "logo" in the traditional sense (i.e., a symbol, etc, for branding). You'll get the letters that you indicate as the "logo text" in whatever font and theme you specify out of a small selection of designs.
Other sites allow a free "trial" of their software. One that I've found to be a good bargain is LogoYes.com. More on that below...
LogoYes.com has a fun, interactive tool which allows you to craft your own unique logo. A few simple steps and you have a professional looking logo to brand your site...
Check out the logo I created for one of my sites using LogoYes.com
It took me an hour or so (only because I'm a touch obsessive) and I was happy to pay the $69 for the logo I created.
Notice that I've used the graphic as a favicon (the little icon to the right of the URL in the top address window) as well, which amps up the professional feel of the site, don't you think?
LogoYes.com also offers a custom design option. Enter your design details and a professional designer will craft 3 different sample logos for you. Choose the one you like the best and work with the designer to refine the style until it's just right.
LogoCare is another good place to go for a custom website logo. They have a set fee of $269. A team of 5 logo designers are assigned to your project. They produce a range of logos for you to choose from and continue submitting designs until one meets your approval.