Free pdf reader that supports taking notes (and bookmarks)

I suggest you try these two programs and choose the one that better fits your needs.

Xournal

sudo apt-get install xournal

All annotations are hand made (so to speak). You can print them on the PDF, if you want, or you can set them apart.

Mendeley

Download from here. Very useful to keep track of your research notes.

Evince 3.6.1 (the default PDF viewer) now supports adding annotations and bookmarks (proper PDF bookmarks), that are saved with the document.

Since Evince 3.14 you can add and delete annotations.

---

UPDATE Evince 3.14: Annotations can be added and deleted.

---

UPDATE 2020: Key S adds a text note and Ctrl + H highlights selected text. (both still require a mouse click to start writing on the annotation). Thanks @Gogowitsch

You could also try Okular. Now you can actually export annotations to PDFs in Okular (this was not possible until recently): http://docs.kde.org/stable/en/kdegraphics/okular/annotations.html

It seems Okular has to be built with Poppler at least version 0.20. It works with Ubuntu 13.04.

Update:

The version of Okular (0.19.3) found in at least Ubuntu 14.04 now also supports customising the review toolbar (the toolbar for adding annotations) by adding and modifying the various annotation types that can be selected.