At some point Firefox 3.6 and Chrome 5 stopped providing the option to download PDFs. To save the PDF, I resorted to using Save As in Acrobat, however, by this point the PDF's original filename had been replaced with a temporary one created by the browser. If you also don't like this behavior, read on.

First, let's disable Acrobat's default of viewing the PDF within the browser. If for no other reason, which there are many, do this to improve the stability of the browser. Disable in-browser viewing by selecting Edit->Preferences. Then, in the new dialog, select Internet under the categories and uncheck "Display PDF in browser." (I also disabled "Allow fast web view" and "Allow speculative downloading in the background.") At this point, when visiting a PDF, Firefox and Chrome will associate a tab with the PDF but will open the PDF in Acrobat outside of the browser.

To enable the choice to download the PDF in Firefox, select Tools->Add-ons. Then under the Plugins tab, disable "Adobe Acrobat." Next, select Tools->Options followed by the Applications tab. Scroll down to the section with entries beginning with "Adobe Acrobat" and change all of them to "Always ask." Finally, test your changes.

To enable the choice to download the PDF in Chrome, enter "about:plugins" into the address bar. Scroll down to the "Adobe Acrobat" plugin and select "Disable." Finally, test your changes.

There are add-ons for Firefox to enable the choice to save PDFs, such as the adware PDF Download, but why install an add-on with the risk of it having nefarious or buggy behavior when a browser configuration is sufficient? One could also remove the DLL associated with the plugin, nppdf32.dll, but this may have unexpected behavior.

I've not found a means to enable downloading of PDFs in Internet Explorer 8.

Software discussed here:
Windows 7 64-bit
Adobe Acrobat 9 Standard 9.3.4
Google Chrome 5.0.375.127
Firefox 3.6.8
Internet Explorer 8.0.7600.16385