You need a news aggregator to subscribe to and read RSS feeds. Some aggregators have additional functionality and most also have mobile apps available. Some popular web-based applications include:
Other types: you can also manage and read RSS feeds using a dedicated desktop application, some email clients, or your web browser. The RSS Compendium list of RSS readers is a good starting point: http://allrss.com/rssreaders.html.
Directories/lists of RSS tools: