On www.kurtsequipment.com in the "Miscellaneous Guitars" section number 11 on the list it mentions Cobain owning a "Lefty Rickenbacker 4001 Bass, natural, which he loved" also in the 2015 Movie "Kurt Cobain : Montage of Heck" on the DVD in the picture gallery you see a picture of Kurt's Rickenbacker 4001 Bass. I believe he used in in early 1994 on the last demos he recorded in the basement of the Cobain residence before Kurt passed away in April 1994.

Paul McCartney is known for using Rickenbacker 4001 basses during the "Sgt. Pepper's Lonely Hearts Club Band," "The White Album," and "Abbey Road" sessions. He owns two: a custom spray-painted version and a natural finish. This usage is evident in The Beatles' "All You Need Is Love" music video available on Apple Music.

In this video Burton can be seen playing a Rickenbacker 4001 in a Burgundyglo finish.

This Bass has been heavily modified with a Gibson EB-0 "Sidewinder" pickup in the neck position, a Seymour Duncan Stacked Jazz pickup in the Bridge position, and a Seymour Duncan Stacked Strat pickup in the chamber for the foam mute under the bridge, activated by a push/pull pot.

This Rickenbacker was Burton's main rig from about Pre-1980 to 1984 and was used in the recording of "Kill 'Em All" and parts of "Ride The Lightning" until it was retired due to malfunction(s). Burton can be seen with this Bass in many pictures from the "K.E.A." tour.

In a handwritten list Burton made for the orginal Metallica Fanclub in the summer of 1983, he lists his gear and modifications as follows:

"Right now, I'm using a Randall 300 watt head into: 1 Randall 1x18 cab and 1 road 2x18 cab."

"At this time I only use 2 effects. A Morley Power Wha Boost and an MXR Limiter."

"I play a Rickenbacker 4001 bass. The 2 stock pickups have been replaced as follows: In the bass position there's a "Gibson EB" pickup. In the treble position, there's a "Seymore Duncan Stacked Jazz" pickup. I have also had a 3rd pickup installed in the bridge. It's a "Seymore Duncan Stacked Strat." Both Duncan pickups are "Humbucking" in design so they help reduce unwanted noise."

On this photo Hans Zimmer plays 4001 Rickenbacker bass guitar

Chris Wolstenholme was seen playing this bass with a plectrum for live performances of Knights of Cydonia and Map of the Problematique. In this video, he can be seen playing live for Knights of Cydonia.

Geddy used his Black Rickenbacker 4001 from their first tour in 1974 until the Grace Under Pressure Warm Up Tour in 1983 although he pulled it back out for A Passage To Bangkok on the Snakes & Arrows tour in 2007 and 2008. He can also be seen using it in the introduction video for the Time Machine tour.

In this photo you can see Les with a Rickenbacker 4001.

Prior to getting his signature model, Lemmy used several Rickenbacker 4000 series basses. As early as his time with Hawkwind, photos show Lemmy with a 4001 in "mapleglo" (natural) finish, already adorned with what appears (an educated guess based on Lemmy's interest in Nazi memorabilia and given the low quality of the photos by today's standards) to be a sticker of a Nazi Reichsadler on the pickguard. https://davidwills.files.wordpress.com/2009/09/bbspeakers03.jpg

Later photos and videos show Lemmy with another, altogether more iconic 4001 with a maple fretboard sporting star shaped inlays, a black pickguard and decals or stickers of an iron cross, some stars and the words "Born to lose, out to lunch". Since neither the fretboard nor the pickguard (and certainly not the stickers) were stock features of the Rickenbacker, this instrument was clearly heavily modified or custom. Motorhead's "The Young Ones" appearance, broadcast in May 1984, shows a bass featuring the "Born to lose, out to lunch" sticker, but with different inlays (conventional dots - the lowest three markers are large Nazi-era German air force crosses, but probably not actual inlays given the size and colouration, which includes the white outline) - most likely this same bass was Lemmy's primary instrument at the time and simply accumulated its various decorations over the course of the '80s.

Lemmy's bass tech, Tim Butcher, refers in one article to having added a fret to Lemmy's 4004LK signature; it appears the same modification was made to the "out to lunch" Ric - in several photos the fretboard either side of the final, uninlayed 21st fret (the 4001 bass usually has 20, and by the traditional pattern of inlaying the 21st fret would be marked) appears visibly darker than the rest of the board. Additionally, the fretboard extends slightly into what would normally be the pickguard. Supposedly, this extra fret is used for the song Metropolis. Since the recognisable modifications seem to appear in the '80s, and it's difficult to identify it with certainty with any pre-modification basses, it's not entirely clear whether this is, indeed, a 4001 model or a 4003, but given the level of modification it's probably a moot point.

"Making shit happen!!! #MeAndRickKickingOutTheJams! @bassplayunited @rickenbackerbasses" Mike on Instagram talking about using a Rickenbacker 4001

paulgilbert_official

I’m playing some bass tonight in honor of my friend, Juan Alderete. Years ago, while working on a Racer X album, I asked Juan to try my Rickenbacker. He liked the sound, but he missed the body contour like on the Fenders that he usually plays. I called my guitar tech, and said “Can you come over, and bring your belt-sander?” We soon had the Rick feeling good for Juan. A few years later, I had the finish repaired, to make it look nice. @j_alderete

In this photo, Geezer Butler is seen playing a Rickenbacker 4001 bass guitar.

Two images are shown during this video immediately after each other, at 12:29, showing Commerford with two different Rickenbackers, a natural finish one with white binding and an arctic white finish one with what looks to be like an gold-anodised aluminium pickguard and no binding ( seems to be a 4001S model due to the dot inlays ).