The first group to record "Hey Joe" was the Surfaris in 1965. In 1965 "Hey Joe" was recorded by The Leaves as well. In 1966 they recorded it again with a fuzztone guitar sound. Also the Byrds, Love, Shadows of Night, Warlocks and many other bands recorded the song in 1966.
A Japanese group called the Golden Cups recorded a version in 1966 that adapted the song to different cultural standards.
Tim Rose recorded "Hey Joe" in 1966, one month before the Leaves' version entered the charts. Rose played the song at less than half the tempo. He changed the key of the song to E instead of A. Rose also roared out the verses, and added his own variant on their structure.
Jimi Hendrix picked up this version of "Hey Joe" and made a European hit out of it in 1967.

This may seem obvious, but for some reason it was a big "eureka!" moment for me: Frank Zappa's "Flower Punk" is not a sped-up parody of Jimi Hendrix's version of "Hey Joe". It is a parody of the earlier, fast garage version(s). Duh!