Heads up or "peeking" notifications, the little miniature pop-ups that appear in Android Lollipop if a notification comes in when you happen to be actually using your device, aren't for everyone. That's why Google will include the option to disable them on a per-app basis in the upcoming Android M release. (See Settings>Sound & Notification>App notifications in the Developer Preview.) It's also why apps like HeadsOff have sprung up to cater to those who want them to go away even sooner.

Unfortunately, it looks like Google isn't all that interested in bringing back the pre-Lollipop equivalent, Ticker Text. Ticker Text is that scrolling text you see across the notation bar when a new alert pops up while you're using your phone, but it's gone as of Android 5.0. (HeadsOff can re-enable this behavior too, by the way.) According to this issue entry on the Android Developer Preview section of Google Code, it's not coming back any time soon.

Thanks for the suggestion. Our development team has looked into this feature request. This will not be included in the M release. However, this may be considered for future releases

The issue was marked "won't fix." So for the time being - and quite likely some time after - Google's engineers don't intend to bringing the Ticker Text behavior back into Android. Root users can already modify this, and ROM developers are sure to take a whack at it once the open source code of the final release comes out, but it's still disappointing for some very specific (and very vocal) users.