Did you ever want to sync your Majordomo mailing list with another address database? Or make it easy for users to unsubscribe using a web interface? Then you will have noticed that Majordomo only offers you a mail interface or an admin tool that you have install on your mailserver. So what if you don't have access to the mailserver?
Then I got the solution for you: introducing Majordomo Web API
I needed to sync an address database in eGroupware with different Majordomo mailing lists (every night). I did this by building a small API that looks like a normal asynchronous API - just with the difference that in be background a mail request to Majordomo is sent and the results are retrieved from an IMAP or POP3 account.
As it always is, our mailing list provider switched from Majordomo to Mailman only a couple weeks after I finished the scripts. So the work didn't really pay off, but I hope it's useful to somebody out there.