At work, my extension is tied into my email. When someone leaves me a message, it's sent as a wav file to my email, and I can listen to it from my mobile device.
Where I work (Google), telephone calls are all but dead and voicemail is completely dead. Pretty much everyone lists their personal mobile number as their phone number in the directory (or a Google Voice number that forwards to their mobile), because getting business calls at home or whatever is a non-issue because no one makes phone calls for business. Communication is via e-mail (for formal communications, messages that don't seek quick response, or group distribution), instant message (for short, timely discussions) or face to face/video conference (Google Hangout). Some groups, especially SREs (Site Reliability Engineers -- sysadmins, more or less), also use IRC, mostly because it stays up when other stuff breaks.
Further, the etiquette is that nearly all non-email communication starts with an instant message. This is true even if the other party is sitting right next to you, unless you can tell by looking that they aren't deeply focused on something. There are only two times a phone is used, one rare, the other extraordinarily rare, and in neither case would voicemail even be useful.
The rare case is for a (generally informal) meeting when one party for some reason doesn't have access to Hangouts. The extraordinarily rare case is when something is on fire and someone's attention is needed at 2 AM Sunday morning. The latter has never happened to me, though I have called a couple of colleagues. Even then, a phone call is an unusual step; normally you wake people up via the pager system (whose messages are delivered via various means, sometimes including automated phone calls) and proceed to communicate via IM or VC.
It's not just Google, either. Prior to Google I worked at IBM which where communication similarly revolved primarily around IM and e-mail, though meetings were primarily via teleconference, not video conference.
From what I can see, voice is generally declining, and voicemail is leading the charge.