If you’re using the digital clock widget, that uses Akonadi, and will launch it on startup. It’s used to (optionally) sync calendar events between compatible apps. There are also a handful of KDE PIM Applications that use it (think Kontact, KMail, KAddressBook, KOrganizer). If you want it disabled, you will need to stop using any Akonadi-enabled app. More information can be found at the KDE userbase for Akonadi. In particular, stop using any KDE PIM Application, as they cannot function without it, and disable calendar syncing from the digital clock. That will ensure the service is never started.
To fix the digital clock problem:
To ensure that Akonadi is not started, check that no applications require it at login. In particular, open the Plasma clock applet preferences, go to Calendar and uncheck Show events to prevent Plasma from requesting information from Akonadi and thus allowing it to start.
Sorry, I’ve revised my comment, so it’s more complete now. As my comment states above, it’s because by default, the digital clock widget (which is placed by default on the task bar–y’know, where it shows the time) has “Show events” enabled by default, which has a dependency on Akonadi. If you uncheck that (and keep in mind that you are using the digital clock widget unless you’ve specifically removed it), and make sure not to use any of the KDE PIM Applications stated above, then Akonadi will never start