How can I highlight or annotate PDFs?
Okular supports PDF annotations.
To save the highliting/annotations directly in the PDF document, choose "File" -> "Save as..." and create a new PDF which will contain your edits.
How to edit in Okular
You can choose Tools > Reviews to get other options like adding
- pop-ups notes
- inline notes
- freehand line drawing
- highlighter
- stamp and other features.
Edit: Inkscape supports PDF editing (one page at a time) and most people seem not to be aware of this so I'm adding it to the answer.
Recently a new version of Foxit Reader is released for Linux. It has the highlighting and annotating support. It has more annotation options than Okular, including inline notes with transparent background, drawing of various shapes etc.
How to install Foxit Reader in Ubuntu is explained in this AskUbuntu answer: Install FoxitReader
Actually, none of these solutions work half as well as anything on Windows or Mac OS. Mendeley only supports yellow highlighting and importing pdfs into Inkscape or OpenOffice is pretty inconvenient if you want to read a paper and simply make some annotations.
Fortunately, there are some free pdf viewers for Windows that work flawlessly with wine (If you find wine too complicated, use PlayOnLinux - a great front end for wine configuration). One of the best of those viewers is the PDF-XChange Viewer by Tracker Software. There is a free version that comes with a ton of annotation features, session saving etc. Grab it here:
http://www.tracker-software.com/product/downloads
And check out this screenshot:
I really wish there was a working open source Linux alternative (xournal is good but too limited). But for the time being, I am happy with using wine.