Create a custom mode to take more control over nonessential notifications, calls and messages. You can still allow designated ...

Maybe you're open to receiving voicemail messages but you don't want to be told each time a new one arrives. To do this, simply disable notifications for voicemails—you'll still be alerted about ...

When you receive a voicemail, swipe down from your home screen with two fingers to fully expand the panel. Tap the voicemail notification and listen to the audio without calling into the service.

Faculty and staff can receive an email notification when a new voicemail arrives. Unlike forwarding voicemail to email, no message recording is attached. If you prefer, you may request technical staff ...

until you've listened to each new voicemail. Aside from playing the voicemail, I haven't found any way to get rid of the Voicemail notification either. This is with 4.3, 4.4, 5.0, and now 5.1.

Update: As promised, this update is rolling out now. Here is the official changelog, per Sprint's forums. Corrects voicemail notification issue (from 4.22.651.2) Corrects issue with hearing aid ...