Can I stop self-pings?

Yes.

Self-pings are found useful by some, annoying by others. Those who find them useful feel that if someone finds the old post that they will see the link to the new post. But some still disagree.

Do this:

To link to this post below

http://faq.wordpress.com/2006/04/20/markdown-textile/

you would normally have that whole url as the link. That will cause the self ping. If you shorten the link to make it relative then the link will work but no ping is sent.

So that long absolute url should be linked as /2006/04/20/markdown-textile/

The same applies to Trackbacks too.

Note: The visual editor may add the domain information back into the link. You can write out your post and before publishing, switch to the HTML editor, remove the first part (ex. http://faq.wordpress.com) of the link, and then Publish.