MS Office and Open-/LibreOffice are using zipped xml files (e.g. .docx, .xlsx and .odt). Svg vector graphics is xml, the x in ajax stands for xml (although replaced by json by now). SOAP (probably counts as the predecessor of REST) is xml-based.

XML was definitely popular in the "well used" sense. How popular it was in the "well liked" sense can maybe be up for debate, but it was the best tool for the job at the time for alot of use cases.