Have one. Everytime a browser requests the file your server has to handle the request for a missing file. Far better to create one, have a positive result and reduce the server load etc. Your logs will be clearer as you'll see the real errors more easily. And it's not like they're hard to create, is it? Why is this the wrong category? Where do you think it should be? You didn't give any info in your question so we're in the dark. From a design point of view the favicon is a branding opportunity so there's no question that it's important.
I am not so sure, but I think browser asks for file only if finds the related meta tag in header, otherwise it wouldn't bother to request one specifically. So you get missing file case, only when one has meta tag for favicon in header and file is not present in its location. Update: I think I am wrong Never mind!