The organ that was popular in a lot of 60s rock was the Hammond Organ, used frequently with a Leslie speaker. The Hammond is a very early form of electric organ, but used an unusual sound system similar to that of an electric guitar, in that it used magnetic pickups and an amplifier. The Leslie speaker is a speaker that has a chamber that rotates at varying speeds, which allows a sort of rotational vibrato which gives so much of that music the distinctive sound.

Now, the short answer as to why the popularity died out is that the Hammond was an earlier technology, and in the late 60s and early 70s there was more variety of synthesized keyboard sounds, with instruments like the Mellotron, the Moogs, and eventually the Yamahas in the 1980s gave you a much wider breadth of sounds to choose from.

The other reason is portability. A Hammond weighs about 400+ pounds, and a Leslie speaker is over 100 pounds. That's a lot of weight for gear when a synth is 5-10 pounds.

The other answer, which also answers your follow-up is simply taste. People's musical tastes change over time, and especially with electronic sounds, an old sound sounds dated very quickly. Think of 16 bit video game music, and every change in digital technology makes the older one look dated. As for keyboards not being used, they're still used quite a lot, but the computer-y sound that's more associated with 80s music was abandoned in favour of sampling - where you take a recorded instrument sound and play it through the keyboard. So a single keyboard can play any instrument in the world, and any possible variety of sounds, and you see a lot of regular instruments replaced by handful of keyboardists playing samples.

I'm not sure that the organ was extremely popular in 60s rock music - the guitar was extremely popular in 60s rock music, and the organ was a frequent featured instrument only in a few 60s bands - The Doors, The Animals, ? And The Mysterians, Procol Harum, Spencer Davis Group/Traffic, Pink Floyd, and a few others. But the organ was a part of 60s rock music, where it had been largely absent in 1950s rock'n'roll.

There's two types of organs that appear in 1960s rock music - there's tonewheel organs such as the Hammond B3 (available commercially since 1954), which generate sound by having a pickup near a rotating 'tonewheel', and 'combo' organs like the Vox Continental (available commercially since 1962), which generate sound using something a bit like an early version of analog synthesis.

The Hammond B3 typically has a warmer, more versatile sound - it has eight adjustable drawbars which vary the volume of different tonewheels with different frequency ranges and harmonics. Hammonds are often paired with a very specific kind of speaker made by the Leslie company, which has a horn-style speaker that would literally spin around at different speeds to give a very distinctive texture to the sound.

In contrast, the Vox Continental has a thinner, buzzier sound - it sounds more electric, and was generally amplified using a guitar amp rather than a Leslie speaker, so it doesn't have the rich texture of the Hammond B3. So 'Light My Fire' by the Doors and 'House Of The Rising Sun' by The Animals use combo organs like the Vox Continental, whereas 'Like A Rolling Stone' by Bob Dylan and 'Whiter Shade Of Pale' by Procol Harum use a Hammond B3.

As to why they were popular, novelty plays a role. Weird, interesting sounds have always been a part of the sound of popular music, and the electric organ sounds of a Hammond B3 and a Vox Continental are both distinctive and novel in a straight pop context in the 1960s. After the organ's presence in popular music became more common, the role of the organ in pop shifted from novelty up-front-in-the-mix kind of stuff; instead, it became something that was used in context of trying to get certain sounds, to be a certain part of the arrangement.

The Hammond B3 had been popularised by the jazz keyboard player Jimmy Smith in the late 1950s, and quickly became a mainstay of exotica music - Esquivel and Martin Denny and the like. However, the Hammond B3 is also an incredibly heavy beast of an instrument, because it was designed to sit in the corner of a church - any band able to take a Hammond B3 on tour with them has a large crew of roadies. So it's only with the advent of much smaller and lighter combo organs like the Vox Continental in the early 1960s that the organ could realistically be part of a fledgling touring band's sound.

To use the Beatles as an example, large studio complexes at the time very often had Hammond tonewheel organs - according to the Kehew & Ryan book Recording The Beatles, the Beatles used a Hammond RT3 organ that EMI's Abbey Road studios purchased in 1960 on almost every album they recorded there. At later Beatles live shows, as can be seen in the recent Eight Days A Week documentary, John Lennon played a Vox Continental at times during the set, complete with glissandos played with his elbow while laughing.

From a musical perspective, organs are very useful as a 'pad' sound - because tonewheel organs and combo organs both continue to make sound at the same rate for as long as you press down the keys, it can be the 'glue' in a song's arrangement, which makes the song feel big and full, rather than sparse. If you didn't notice organ on most of the Beatles' discography (outside of the Let It Be album, where Billy Preston's organ playing is deliberately very prominent), that's because it was usually being used as 'glue' in this context - it's mean to support the song rather than draw attention to itself.

I would have argued that while the organ became less of a up-front feature of songs in the 1970s, the way they are on 'Light My Fire' or 'House Of The Rising Sun', that organ sounds are nonetheless probably more common in the 1970s than in the 1960s simply because they made a fantastic pad sound. Everything from 'Us And Them' by Pink Floyd to 'Hollywood Nights' by Bob Seger to 'Refugee' by Tom Petty features organs used as pads. Bruce Springsteen's E-Street Band had, basically, a full time organ player, Danny Federici, as well as a piano player, as did The Band (Richard Manuel) - listen to Springsteen's 1975 'Thunder Road' or The Band's 1975 'It Makes No Difference' and you'll hear organ. And those are just the songs where it's perceptible; plenty of songs feature organ low in the mix for that 'glue' effect. Though there are also certainly some 1970s rock bands where organs are still prominent parts of the sound - most obviously Steve Nieve playing a combo organ in the punk/new wave band Elvis Costello & The Attractions, or Jon Lord's organ crescendos in the progressive rock/proto-metal Deep Purple.

As to the organ getting abandoned, the rise of the polyphonic synthesiser - keyboards like the Korg Polysix or the Roland Juno - in the late 1970s and early 1980s gave rock bands other options for that pad sound needed to be the glue in the arrangement, and so you get, say, The Cure using a pad synth on the 1986 track 'Just Like Heaven' rather than an organ.

Nonetheless, the rise in the 1990s of bands that aimed to emulate a 'classic rock' sound from the 1960s or 1970s meant that the organ came back into vogue - if you want a pad sound on a song, a Hammond B3 did that sound in a more 'classic rock' way than, say, a Roland JX8P synthesiser. And so, since the 1980s, there have been Hammond B3 emulator keyboards, specificallly designed to emulate a Hammond B3 going through a Leslie speaker, complete with adjustable drawbars. So, in rock, there's Hammond B3 all over a commercial rock song from the mid-1990s like The Wallflowers' 'One Headlight' - and while the Wallflowers' keyboard player probably played a vintage Hammond B3 in a studio, he likely used an emulator live.

Also, for what it's worth, outside of being an AskHistorians moderator, I do a bit of session keyboard work. Almost all of the commercial recording studios where I've played still have vintage Hammond tonewheel organs sitting in a corner next to a Leslie speaker. Today I played a vintage 1961 Hammond tonewheel organ on every song I recorded keyboard parts for.

Can I ask a follow-up: what factors led to the abandonment of keyboards in general in rock music after the '80s?