I recently ran into a problem whereby I was trying to run a 64-bit Java application and yet I only had a 32-bit edition of Java installed on my 64-bit Windows computer. To obtain a 64-bit copy of Java I needed visit the Java download page using a 64-bit browser.
On visiting with a standard 32-bit edition of Internet Explorer, Firefox, Chrome, etc you’re only be given the option of downloading the 32-bit compatible plug-in. The probable reasoning behind this was to avoid confusion with 64-bit Windows owners. Who might not realise that their browsers are 32-bit programs running within a 64-bit operating system, making the 64-bit plug-ins useless.
As of writing there are currently are no active 64-bit Windows editions of Chrome, Firefox or Opera. Microsoft conveniently includes a 64-bit copy of Internet Explorer 7/8 in all 64-bit editions of Windows Vista and 7. Doing a quick Windows search for ‘Internet Explorer’ or ’64-bit’ should reveal it and with that you should be able to obtain a 64-bit edition of Java. You should also be able to install and run both editions of Java on the same operating system.
Now I have the correct edition of Java I can run the 64-bit version of Eclipse 5.6 (Helios) without any of the cryptic “Failed to load the JNI shared library” errors!
The Developer's Tidbits 
Thanks for this; been having trouble installing Charles Web Proxy at work for the very same reason. Much appreciated!
Thank you, my first foray into java/android development was about to end in a 30 minute swearing session.