64-bit CPUs have existed in supercomputers since the 1970s but have only recently entered the mainstream of personal computers.
The maximum memory address for 64-bit computers is 264, which is 18,446,744,073,709,551,616, which is 17,179,869,184 GB. As a practical matter though, many operating system like windows will still allocate only 2GB of memory to a process (or 3GB is some cases) so it is still possible to get out of memory errors when in fact, there is plenty of memory left.
The usage of 64-bit processors solves a multitude of practical issues, including the ability to address more than 4GB of RAM on computers and the Year 2038 problem.
Keep in mind that while the OS you are using maybe 64 bit, the applications you are running may still be 32 bit. This is true in Windows, Linux and OSX.
