The song has its origins in Bobby Pickett's rather remarkable impersonation of Boris Karloff's voice. One night while performing with his band The Cordials, during a performance of The Diamonds' song "Li'l Darlin'," Mr. Pickett went into his Boris Karloff impersonation. The performance received accolades from the audience to the point that fellow Cordial Lenny Capizzi urged Bobby Pickett to continue utilising his Boris Karloff imitation in performances. As a result, Bobby Pickett and Lenny Capizzi recorded '"Monster Mash." Their backing group, credited as The Crypt-Kickers, consisted of Terry Berg, Johnny McCrae, Rickie Page, Gary S. Paxton, and pianist Leon Russell.
"Monster Mash" was released on 25 August 1962. During the week of 20 October 1962, right before Halloween, "Monster Mash" hit #1 on the Billboard Hot 100 chart. What is more, the song would hit the Billboard Hot 100 three more times: in December 1962, August 1970, and May 1973. The song would also be covered several times. A notable cover version was performed by Boris Karloff himself on the 30 October 1965 episode of Shindig (the original footage of which has been lost). It has also been covered by The Beach Boys, The Big O, The Misfits, Smashing Pumpkins, and even Vincent Price.
Here, then, is the original version of "Monster Mash" and Bobby "Boris" Pickett and The Crypt-Kickers.
Here is The Misfits' cover version, combined with footage from Rankin/Bass' Mad Monster Party.