It's free and open-source. I think it started off as a bibliographic manager, but has expanded well beyond that to a library and file of notes. You can grab the citation (usually a painless single click), and stash the pdf (usually grabbed automatically) and your notes (via a built-in editor) underneath the bibliographic entry. If it is a webpage, zotero grabs a snapshot. You used to be able to annotate webpages, but that function seems to have been recently dropped.
Once you have the entry, you can tag it. You can also have another
level of organisation by creating folders of citations. I use tags
mainly as permanent keywords (except for workflow-related tags like "To
Read") and use folders for specific projects, which I delete when I'm
Creating a citation and bibliography in a document is just a matter of dragging and dropping, but for more involved work there are dedicated plug-ins for Word and OpenOffice. If you remember doing bibliographies manually, this is science-fiction, the kind with jet packs and flying cars.
You can sync your Zotero library among multiple computers using a remote server. Zotero.org has limited space, but I use JungleDisk (for about $8.00/month).
There are a couple of other Zotero-related applications that I find indispensable.
The main one is Zotfile. This is an add-on that manages the pdfs attached to the references. It will automatically rename pdfs to something a little less cryptic than the usual downloaded article filename. You can set the renaming rules, but the default author's-surname_date_title works for me.
If you use a tablet for reading, Zotfile will send the article you want to your tablet via Dropbox. Read it on your tablet from Dropbox, mark it up and annotate it, and, when you are done, use Zotfile to retrieve it from Dropbox back into Zotero.
Zotfile will then extract your mark-ups and annotations and create a note under the bibliographic entry!! This is brilliant. Zotfile is free but you should definitely make a donation.
On my smartphone (Android) I have Scanner for Zotero. With this I can scan a book's barcode and upload the bibliographic information into my zotero database.
Obviously I have an 8" Visio Android tablet (a Costco special) for reading pdfs. I use ezPDF Reader for this task. It's not free ($2.99), but worth every penny, and more. It's the best app for marking-up and annotating PDFs. As I noted earlier once you are done, Zotfile can go through and create a text file from your highlighted or underlined sections, and your marginal notes.