If you use the hash instead of a question mark in a URL, whatever comes after it will not be indexed. This can help with de-duplicating content.
Canonicalisation – rather than having many copies of pages that are essentially duplicate, you can reduce it to flow the link juice to one main page.
Affiliate URLs – instead of having each affiliate linking to each of the different versions, have them all point to the hash. Then it’s up to the search engines as to whether they count them or not.
Showing limited content – for example, you only want people to be able to see the first page of your article, rather than the engines indexing all the pages.