RSS in action:
The State Library of NSW has a page of RSS feeds to subscribe to. The feeds are concerned with communicating that new titles have been added to the collection, and are sorted by categories such as language, subject and format. Some of the languages mentioned would probably not be in circulation in local libraries (e.g. Tamil), so it would be beneficial to a local library service such as Newcastle Region library to subscribe to that RSS feed if their users were requesting Tamil language books for interlibrary loans. The Library also maintains an "About RSS feeds" which describes in simple terms how RSS works; this would be helpful for new users of RSS.
The University of Cambridge includes RSS in its Library toolbox; users can subscribe to feeds like "Any downtime we are planning", and a Library Widget which shows due dates for library loans in various calendars or in their RSS feed; it also includes instructions for each type of compatible calendar.
From these two examples, there are many ways an RSS feed can help to meet the information needs of library users. The due dates RSS feed would be useful for traditional loans, by providing convenience to users by not needing to log on to the library's catalogue separately.
In searching for two examples, I went to the New York public library page, and while it maintains a presence on all the major social networking platforms, I could not find an RSS feed for them. I then went to the National Library of Australia's page (NLA) and also could not find an RSS feed. The NLA does have a published social media policy online though, which will be a useful resource later in this subject.