A google search finds various sites that offer house sitting such as trustedhousesitters.com
A screen grab as an example as I know we cant post links to some sites.
(names blanked out in red)
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The problem I see from a homeowners perspective is that a lot of the people are young and will have never have owned a home and might not have the same respect for someone's house as the person that has struggled to pay for it.
Not wanting to sound harsh with that.
Also the possibility of inviting friends round and having a party.
What if the house sitters are smokers, the house sitting websites say how good the people are with cats and dogs but forget to mention smoker or non smoker

That has to be the first question doesnt it, a non smoking home owner wont want someone smoking in their bed will they.
A few issues to think about.