Our (TOM) nightstops (not days off) vary massively. In Summer it's mostly 24-48 hours downroute, in Winter we fly for our European airlines a lot more and night stops are anything from 24 hours to 7 days. The longest trips are 10 days as these will involve various amounts of positioning. For example, we have a run of flights through Winter along the lines of UK - Hamburg - Dominican - New York - Barbados - UK with several days in various locations along the way. This is fairly common for us.
Or we have loads of UK - (insert any Scandi Capitol City) - Thailand for 3-5 days - (Scandi city) to UK.
if we are rostered 10 days away (or more I suppose) we will be given official days off downroute as we are not allowed to work more than 7 days without a day off.
I hope that helps.