Can I hide a program from ongoing activities in the notification bar?

Try Smartbar. I used to use it and it allows you to put shortcuts in the notification bar as well as hide icons in the notification bar. I can't remember off the top of my head if it hides the icons put there by other apps but I think it does. Sorry for the cheap answer, I just can't remember and I don't have time right now to download it and try it out to be sure.

I would talk to the developers of apps and ask them is they plan to include the option to remove the app from the notification bar. They may oblige such a request. You could also leave a comment for the app and add that as a side note.

CM team and other ROM developers do create flashable updates to their ROMs so that icons and other items can be removed from the notification bar, but they usually do not do this for specific applications. You could check out information on this in the forum of the ROM you are using.

As of Android 2.0, the system requires that apps that run constantly in the background, and that require a certain level of priority so that they don't get killed offhand (like music apps), put an Ongoing Notification. This was to prevent abuse of requesting this level of priority without letting the user know that it's occurring.

You can read about this here: http://developer.android.com/reference/android/app/Service.html#startForeground(int, android.app.Notification)