I want to run MAMP on my Windows 8.1 pc, but when I start the servers, it says:
\'APACHE\' needs open port \'80\' which is already being used by another
service
If you arrived here because you just installed MAMP on a Windows OS (7~10), then Microsoft IIS is the most likely culprit hanging on to port 80.
You can confirm that with the CLI netstat advice by Sergio below and should you find via netstat that a listening service has a process id that maps to NT Kernal & System (ntoskrnl.exe -> cross check via details tab in task manager) then the culprit is IIS.
To Turn off IIS;
Start menu -> Control Panel -> Programs & Features -> Turn Windows Features On or Off -> De-select 'Internet Information Services'.
If you know why IIS is running then you will likely know the application that specifically needs it and you can turn back on when need (take note of the selection chain when turning off) -- otherwise it's unlikely you need IIS on.