There are two prominent implementations of MPI that can be used on the Raspberry Pi. These are: OpenMPI and MPICH.
OpenMPI is an open source implementation of MPI maintained by a collection of industry and academic partners. It has been implemented on a number of the world's top 500 supercomputers including the Japanese K computer.
OpenMPI's origins can be found in several other projects including the University of Tennessee's FT-MPI project, Indiana University's LAM/MPI, University of Stuttgart's PCX-MPI, and LA-MPI from Los Alamos National Laboratory in the USA.
You can find out more about the technology at the official website:
MPICH, originally standing for Message Passing Interface CHameleon, is an implementation of the MPI standard that supports C, C++, and Fortran applications. It was initially developed in the early 90's to provide feedback on implementation issues to the MPI forum.