Just one example from recent practice, to automatically collect a number of texts (pdfs) into a set of groups for easier subsequent processing (summarization). Without K-Means you'd have a pretty hard time figuring out for each subsequent document which group you want to add it to or whether or not you need to make a new group. With K-Means given a fairly simple 'distance' function all of the grouping is automatic. In fact, once you have K-Means coded up the distance function is the problem to solve. If you can't meaningfully define a distance then you probably won't be able to use it.