I installed the PDFjs plugin from Mozilla for Firefox. As the name suggests, this is a plugin for opening PDF files within the browser. It has been working really nicely for me and has opened some PDF links I tried just fine. I am using this on Linux, though it will probably work just fine on other OSes as well as it is written in Javascript apparently.
Get it here: https://addons.mozilla.org/en-US/firefox/addon/pdfjs/
The description says it can't open some files, such as password-protected ones, but you are likely to download and open those locally anyway.
Unstable PDF reader plugins begone