If you have a WordPress.org site but want to install Akismet on it, you will get a page informing you that 'you need to have a WordPress.com' account in order to get an API Key.
This may lead you to think that you can only use Akismet on a WP.com site, but this is not so. Even if you have a WP.org site, you 'still' need to open a WP.com account. Once you have done this you can log in to Akismet with that username & password.
The Akismet Key will then be sent to your e-mail address that you used when registering a WP.com account. You then just install Akismet in your WP.org site as usual (install a plugin). Go to the 'edit' menu where the plugin is stalled and copy and paste your new API key into the required 'serial number' window.
That is it.