@MMike and @PHeMoX: I see your point, but the question asks for which of them you consider "most important" so basically it asks for the features that are most essential in a file browser which, if they weren't there, would prevent you from using it. I agree though that all of them are important.
Yeah, it that case; renaming files and being able to copy and past them (or duplicating files for back-up purposes) is rather vital for me.
A search function comes in handy, but not necessary, my files data bases tend to be not huge.