Use if .. else if .. statements for this purpose. However, formula fields support case syntax, but it eventually compiles into an if ... else if format
Depending on the requirements you may be able to solve it by using Case formula in a workflow field update or formula field (workflows have larger compile size than field formulas) and then use that field in a trigger to fire off the remaining logic. I did it with the Case priority field and it works great with just three lines of code
Apex does not support switch case statements.
Use if .. else if .. statements for this purpose. However, formula fields support case syntax, but it eventually compiles into an if ... else if format