Adblock Plus

I'm not sure this will work on every device, but it works on my nexus 7 running 4.2

Slide down the notifications bar and long press on the adblock notification. That will take you to the app's info page. In there, uncheck the option that says "show notifications". That's it! Adblock continues to run in the background without problems and block everything.

Let me know if this works for you.

Confirmed on my Verizon Galaxy Nexus running CyanogenMod 10.0.0. I'm pretty sure this will work for any Android 4.1/4.2 device... possibly earlier as well, but I don't recall exactly which version added the "show notification" checkbox to app settings.

I have a Droid Bionic running ICS and it doesn't give an option to change notification.

Don't see the option anywhere on my S3... I would love
to be able to clear the icon as my notification bar is often very full..

This is a jellybean feature only. (silence notifications)