The LLVM logo is a stylized wyvern (a kind of dragon). Dragons have connotations of power, speed and intelligence, and can also be sleek, elegant, and modular (err, maybe not). In addition, there is a series of influential compiler books going back to 1977 which featured dragons on the cover.

You can also download a larger version of this image here.

LLVM used an older dragon logo for many years. This version is endearing for many reasons, including an unproven theory that it has its head upside down (and an anonymous Australian takes the controversial view that its body is actually upside down)!

Here is the image in a couple of sizes:

Here are several derivative versions of the dragon logo, which may be more suitable for use as icons etc. These were contributed by Teresa Chang: