I have a South Africa passport. What is the maximum multiple-entry visa I can get for Europe with a UK work permit? Does the permit improve my chances of getting a longer travel visa for Europe?
The maximum validity of a Schengen visa is 5 years (article 24 of the Schengen Visa Code). What you get is left at the discretion of the consulate to which you apply but I think a UK work permit does indeed improve your chances of getting a multiple-entry visa valid for a year or more.
Note that you cannot in any case stay more than 90 days in any 180-day period (and therefore stay for than 3 months at once) with such a visa, even if it is valid for 5 years.
I think Romania, Bulgaria and Croatia have similar regulations. I don't know about Cyprus and other non-Schengen countries.