In modern day, dogs are referred to as "man's best friend". From my experience, most of the times dogs are companions and aren't necessary for survival. Although we do use dogs for many work tasks (seeing eye, bomb sniffing, etc) these roles seem modern and not jobs that would've been done/needed historically.
In movies depicting the Victorian era dogs are often depicted hunting with the wealthy, but for game rather than pure necessity. Were there cultures or times where dogs were necessary (or at least very valuable) to survival?
Groups of people who live in Arctic regions have relied heavily on dogs for at least 4000 years. Dogs were used to help carry supplies and pull dogsleds Im not sure how important dogs were to cultures outside of the arctic regions though. Off the top of my head I can't think of any non-arctic based cultures who were heavily reliant on dogs. Dogs certainly played an important role in the arctic though.