Android - How to disable Heads Up notifications in Android Lollipop? (notification popup at top of the screen)

A non root option is now available. The HeadsOff app can disable all Lollipop Heads-up notifications on your phone. It can also disable Heads-up notifications only for selected apps. If you purchase the Pro key you can restore the ticker text in the status-bar to see a little notification preview.

On Cyanogenmod 12.1+ (including CM13) there is by default an option to enable or disable heads up notifications. Just go to Settings -> Notifications -> Heads up There you can enable or disable the heads up notifications.

Another possibility is using adb:

adb shell settings put global heads_up_notifications_enabled 0