You can add GitHub logos to your website or third-party application in some scenarios. For more information and specific guidelines on logo usage, see the GitHub Logos and Usage page.
You can also use an octocat as your personal avatar or on your website to link to your GitHub account, but not for your company or a product you're building. GitHub has an extensive collection of octocats in the Octodex. For more information on using the octocats from the Octodex, see the Octodex FAQ.