Zotero is an open source citation management software that saves citation using a browser plugin. Zotero has the ability to detect citations in many different formats, and will automatically download the associated PDF. If there is no PDF, Zotero will save a copy of the webpage that can be accessed while offline.
Zotero allows organization using both folder and tags, and has options for shared folders for collaboration.
Zotero operates on a freemium scale, with the first 300MB free. Citation information and un-synced files do not count against your storage space.
Mendeley is a software offered by Elsevier that saves citations and PDFs using a browser plugin, then allows you to organize those citations in folders and cite them using a word processor plugin. Mendeley will also search PDFs for citation information using DOIs and other identifiers.
Mendeley also offers more of a social experience, with the ability to join groups and see citations for those groups. You may also create private groups, with a maximum of three members, for group work.
The first 2GB of storage is free; after that pricing runs is 5GB for $55/year, 10GB for $110 /year, and unlimited for $165/year.