To make a logo, you can click on a tag for a subject of your choice to find relevant templates. Tags include a wide variety of topics from "animals" to "industrial" to "technology" to "wedding." Once you select a template, you use the on-screen editor to change colors, add text, etc. In order to download your image without a watermark, you need to register at the site, but registration is free and just takes a few seconds.
Here's a little logo I created when I tried out the site. Cheers to Free Logo Wizard!