I'm currently trying to create a little app that should run in background. It should start with the system or springboard and run until the device shut's down. I searched for tutorials out there but doesn't found anything really useful. It would be great if someone would help me out.
Best regards
EDIT: I'm sure that it isn't possible in an app designed for the appstore, but i'm looking for a variant that work's on jailbroken devices.
ColinE's answer is wrong. SuperDev's is correct. You certainly can create services on iOS, just as on OS X.
As another reference, the best tutorial I've found on the subject is Chris Alvares' blog post on creating an iOS Launch Daemon. (Launch Daemon is the proper iOS terminology for what you're describing)
You may find additional useful information within the Apple Docs for Launch Daemons, or searching for OS X information, instead of just for iOS, where it requires jailbreaking (and therefore is less widely used).
Cydia has lots of apps that are launch daemons, or contain launch daemons (possibly in addition to a UI application).