Whenever I set up a new account on KMail, mysqld + akonadiserver start using 100% CPU time, with no reason specified anywhere (eg. the GUI).

What's it doing? Indexing? How do I stop it? Why doesn't the GUI specify what's it doing?

Some users (and that includes me) will think KMail is just misbehaving, and then will kill those services right away, which will make KMail break, I suppose.

MySQLd and Akonadi Server shouldn't start using 100% of the cpu for no reason at all. Are there other applications using moderate/high levels of CPU at the same time? Possible suspects include Nepomuk, and KDE PIM applications.

It largely depends on what kind of account you have. Do you use IMAP (disconnected or online), or POP?
As bcooksley said, likely the spike is due to the initial indexing of the emails, which can be long if you have many. In 4.8 you'll be able to turn indexing off if you don't need it, however.

It was after adding a new IMAP online account. I have ~5000 mails only so I don't think this should happen. After six hours of continuous 100% cpu use, I restarted the Akonadi server with AkonadiTray.