My Samsung Galaxy Mini has an app on it called "O2 Menu". I did not install it, so I can only assume it was installed by the vendor prior to selling it to me (the phone is on Tesco Mobile PAYG, which appears to be provided by O2, so this seems plausible). This app does not have any user interface as far as I can see (it certainly doesn't have an icon in the launcher), yet it runs on my phone constantly, restarting instantly if I "force close" it. It has a very liberal set of permissions.
What does this app do? Is there any way I can stop it (my phone is rooted)?