The very first recording of the song was by Johnny Darrell on California Stop Over (1969), an album which was reissued as a part of Singin it Lonesome (2000)
Other artists who have covered "Willin'":
The Byrds on the box sets (Untitled)/(Unissued) (1970) and The Byrds (1990)
Commander Cody on Commander Cody & His Lost Planet Airmen (1975
David Allan Coe on 20 Road Music Hits (1997)
Steve Earle on Sidetracks (2002)
Flying Burrito Brothers on California Jukebox (1997) and Honky Tonkin' (live) 2002
Chris Jones on Free Man (1998)
Dave Kelly on Willing (1979)
Gene Parsons on Kindling (1973)
Linda Ronstadt on Heart Like a Wheel (1974)
Jim Yeomans on There Goes My Heart (1996)
Jon Randall on Willin' (1999)
Seatrain on Seatrain / Marblehead Messenger (1999)
Richard Schindell on the live album Courier (2002)
Show of Hands on Covers (2000)
Cover versions performed live include The Black Crowes, also Ry Cooder has performed it with Little Feat.
sighmoan says: The story goes that when Lowell George was a member of The Mothers of Invention, he played this song for Frank Zappa, and Zappa told him to quit the band and start his own group. Zappa broke up The Mothers shortly thereafter, and George took their bass guitarist, Roy Estrada, and formed Little Feat.
"When he played it to Zappa, he was told that he had better quit the Mothers and form his own group." (Ben Watson: Frank Zappa. The Negative Dialectics of Poodle Play St. Martin's Griffin Edition, 1996, page 520)
Sources: various, notably http://www.littlefeat.net/lfc.html, All Music Guide and cdnow.com. Know of more cover versions? /msg me, please