In our Trademark Guidance we say:
The logos associated with Stack Exchange Inc. and any Stack Exchange site are a trademark. The purpose of trademark law is to prevent consumers from being misled as to the origin of a product. So if you were making a product, and you used a Stack Exchange name or logo in your product (or in its advertising) in such a way that would mislead someone into thinking that your product was owned by, operated by, endorsed by, or in any way part of Stack Exchange Inc., you would be violating the trademark and this would not be legal.
Our logo images and site names are copyrighted. Any content on the Stack Exchange Network not contributed by users is copyrighted. Copyright is different than trademark. Ordinarily you couldn't copy it. But if you were writing a news story or blog post about a Stack Exchange site, reproducing the logo image would almost certainly be considered "fair use" and allowed under trademark law because you were not using it "in trade."
The logo is copyrighted by Stack Exchange, as can be seen in the legal notice on StackExchange.com.
The Network and its contents are intended solely for the use of the Network Subscribers and may only be used in accordance with the terms of this Agreement. All materials displayed or performed on the Network, including, but not limited to text, graphics, logos, tools, photographs, images, illustrations, software or source code, audio and video, and animations (collectively, “Content”) (other than Content posted by Subscriber (“Subscriber Content”)) are the property of Stack Exchange and/or third parties and are protected by United States and international copyright laws.
This can also be seen in the footer:
site design / logo © 2013 stack exchange inc;