• Works with most browsers (all, via somewhat limited Zotero bookmarklet)
• Works with wide variety of content types, including website
• Saves PDFs and screenshots ; can attach any sort of online file (although may not be searchable)
• Saves bibliographic information, notes, tags, and related items
• Searchable - no more silos
• Useful after you graduate - retain everything, add more 

Web Access

• Optional
• Allows you to access your Zotero Library online, and sync your items between different computers
• Can just save bibliographic data and notes (free) or add attachments like screenshots and PDFs ($)
• Basic citation generation
• Can add or edit online (but better to use the Zotero Bookmarklet if you are adding multiple items, although it doesn't work with all source types)
• Can use Zotero's group functionality (...you might be able to use this somewhat just via a Zotero account...)
• Latest update makes it look just like your desktop/laptop Zotero interface

Third-Party Tools

Zotero's open source-ness has created a pretty rich ecosystem of applications and tools that work with it. Here are a few, and you can find more on the Zotero Plug-ins page

• Do you have a tablet of any kind? Just using Zotero.org works well, and you can open, read, and annotate your PDFs in PDF-reading apps like iAnnotate or PDFExpert  #Requires use of Online Zotero.  (Alternatively, ZotFile creates a nice workflow for moving your PDF to your tablet app to annotate them, then moving it back.)

I'll be adding more to this - I'm trying to make a series of shortish (around 20 minutes) screencasts that demonstrate Zotero.

As a open source tool, Zotero has a robust number of third-party add-ons (plug-ins) that really make it even more useful. You can find a (not comprehensive?) list on Zotero's Documentation Page.

I have started some demo videos for these below.

Here are some additional videos (some I created, some from Zotero's documentation, that may be of use).

12/22/17: This was created as an aid for two webinars I did for WSU's Global Campus. (Links below). It was before Zotero's big 5.x update, so this will be slightly out of date, although mostly still usable.

8/2018 update

• A two-hour screencast recording of a class I taught in the fall of 2017