What file format should I use to format my new external HDD? I've just purchased a WD Elements external hard drive and plan to use it across Linux, OS X and Windows devices (read and write on every OS).

Is there any file format by which I could format my HDD so that I could read and write across all these OSs?
FAT32 works on every system, but files cannot be larger than 4GB in size.

There is exFAT, which works with larger files, but it isn't natively supported by Linux. You can however see this link how to get it working on Ubuntu for example (read and write support with this solution).