Majority of web designers are facing necessity to develop logo for their sites. For many of them this is just small part of the work. If you don't want to outsource logo design job and don't consider yourself to be an experienced graphic designer, my approach can help.
I'm definitely not a graphic designer. Adobe Photoshop or GIMP (open source, free equivalent to Photoshop) doesn't look like a simple solution for me when I have to make logo for a new site. It seems to be very easy thing to do. But it is not. This task requires talent, knowledge and a “good” taste.
I'm using Cool Text to make Logo's. It is easer to use some predefined styles and methods and make some changes afterwards. This is not very flexible but provides a possibility to do something basic that would possible fit into your web design.
Final result could be downloaded in a couple of different formats including Adobe Photoshop PSD with layers and could be a good base to start with. Then you can edit this file in Photoshop or GIMP to complete your Logo.
Cool Text also offers more than 1000 different free fonts that could be downloaded and used for your graphic design needs.
This article was also helpful in my logo design efforts:Simple Logo Designs Using Photoshop