How often do you hear emergency vehicles near your home? They are common here as we live close to a hospital.

Never. 

At work, everyday. My business is on a main route (root) to get to hospital or police. 

Never near my home, I can’t think of a time I’ve heard at work either and that’s in the city. Maybe I block it out. 

Here it is a feature of the environment. It is remarked upon, one of the familiar sounds of the place. We heard less of it even living on a major artery in the heart of a smallish city (2.7million people) a few years ago, a city milling with people and traffic at all hours of day and night.

  Not very often at all.  We live about four blocks from a main street, and within a half mile of an expressway.  Both of them run parallel in a north-south direction in relation to where our house is, and there are a lot of others other residences between ours and the main street.  The expressway is situated a bit downhill from our house, and there's a retaining wall that runs along it, so we don't often get disturbed by the sounds of traffic in general, or specifically by sirens.
  Of course, it could also be that in the time since the expressway was completed, about 15 years now, we've merely become accustomed to the sounds and subconsciously dismiss them.  When my wife's brother first came here to California from Florida on vacation a few years ago and stayed in our guest room, he couldn't sleep at all, citing the noise of the expressway's traffic.
~ This post was edited by Randy D at October 28, 2020 8:31 PM MDT

Almost never. 

Probally  at least 10× a  day 7 days a week.  Stupid part is when my dog was a pup I taught him to do the wolf howling at the moon thing whenever he heard a emergency vehicle go by.  Back then we lived in  a place that rarely had emergency vehicles go by so it was funny but it's not so funny now. Cheers! This post was edited by Nanoose at September 5, 2020 7:38 AM MDT

Not too often considering there are many retirees here and my house is only a couple miles from a fire station.  Crime is low too.  I do from time to time see and hear cop sirens when I'm out and about but from home I think I always assume a siren is a fire truck or ambulance.