Apart from stuff like The Wild Rover, it largely depends on the quality of the singer. There are songs, like 'Kilkelly', of which there is only one version I can stand.
Of course, if you've only ever heard one version, that can work against a song, too. It didn't take me long to get fed up with 'Waltzing With Bears', sung by Ann Mayo Muir - but then it's got such a remorselessly sweet tune I can't really imagine liking any other version!