You need to setup the browser's "viewer" for pdf files, if you don't have the plug-in installed for the browser, it won't show the PDF for that browser. Also it is a question of how well the web site is written to be able to communicate to the web browser that the content coming across is a PDF file.
See when you view content on your web browser there is a bit of negotation that goes on between the web-server and the client. It is possible, as I recall for the web server to ask what formats it supports, but often is the case that the files are sent over raw, and the web server looks at the file suffix before it sends the file to determine what MIME-TYPE to put into the file-send header.
The MIME-TYPE is a human readable phrase about 40 characters long at most, categorizing the data-type of the file being delivered, the response of the client is to view this content in the browser if it can match the MIME-TYPE the server gives it to the plug-in that handles this type. If the MIME-TYPE has typos in it or it is not one the plug-in doesn't recognize, the last resort is to store the file on the drive.
It used to be the case that you could browse a list of the MIME-TYPES and their file suffix correlations in the web browser but finding this list is harder, and well-designed websites turn to using embeddable objects in their web-content that more precisely define what to do with the content, such as notifying the user if they lack the plug-in with which to view the content.. But if you try to view a file say from a server folder listing or from a remote email server, if it isn't Google mail, and your browser's PDF plug-in doesn't reciprocate the server's MIME-TYPE for the file being sent, then the file will notified to you to be saved to the drive.
In the old days, before plugins you would define for the browser the application and command line parameters used to view that file. That functionality still exists though it seems dumbed down. In Firefox you will find it in "Preferences -> Applications", the quasi-MIME-TYPES (these don't look right) are on the left and the application to use is on the right. This may be different for firefox on Windows, I'm in Ubuntu 12.10 Linux right now so I would have to reboot into windows to try it out.
As I recall the MIME-TYPES handling in IE is shared with Microsoft's filesystem, you need to look up how to handle mime-types in the filesystem in windows I think, if you want to automate the load behaviour.
BTW, "about:config" in the address bar of firefox will show you all your firefox settings. The "void warranty" is an inside joke placed by firefox staff, it's inspired by Microsoft's attempt to close source the PC platfom by making hardware inaccessible to users otherwise you could void your warranty by opening the machine.