Only? No way! :D
The Roland TR-909 is also extremely popular and was considered the sound of techno and house even after the TR-808 started to fade outside hip-hop. In the mid-90s it was one of the first drum machines to start being cloned by new manufacturers due to the demand. The bass drum is still used as the foundation for a lot of EDM. It never went away... while the 808 which is back but was considered passé even in hip-hop for a short while.
The TB-303 Bass Synth is also extremely sought after. It was the sound of Acid House in the late 80s and was also a mainstay in the 90s for a lot of producers, even though it's limited. Today it's kind of a novelty but you still hear it in some tracks. More recently Behringer made a clone and Roland reissued it.
Both of those two got in the vernacular of EDM fans at the time.
Also the TR-606 has some cult status due to being used by artists like Autechre, Aphex Twin and Plastikman among others, which are sort of "musician's musicians" among the electronic music crowd, although it wasn't as famous as 303/808/909 among general listeners.
I am also a big fan of electronic music and owned several of the x0x synths, but they're only really recognizable to people who are already into synths. Of course if you play an 808 and 909 next to one another, they don't sound the same. But if you play a random piece of music and ask a casual listener what drum machine it features, I don't think they would be able to tell you. (Unless, perhaps, it's an 808!)
Even something that synth nuts know to be as unique and genre-defining as a TB-303, to the casual listener it isn't distinguishable from an SH-101 or any other analog monosynth. People might know what an acid line sounds like, but they don't tend to have the same kind of ear that musicians do to be able to spot one synth model from the other in the final mix.
When I think about a synth so distinctive and widespread that it changed modern music, I think about something that average people who aren't musicians can identify. The DX7 might have been that, since it was the first synthesizer that really went mass-market. All the synths before that were "niche" instruments, but the DX7 made synth music mainstream, so perhaps it was very identifiable. But then the floodgates opened, so it might only have lasted for a few years.
The 808, though, I think a lot of people still really know and understand what kind of "sound" that is. But I could be wrong.
A lot of pop from before was already using synths. Funkytown was a Billboard #1 hit 4 years before the DX7, and so was Vangelis, Human League, Eurythmics and Owner of a Lonely Heart a year or two after that, not to mention lots of Michael Jackson and even the Ghostbuster theme... and that's just the Billboard #1 hits. Even Van Halen released "Jump" a year before the DX7, and England was already having synth bands since the late 80s. People were more than used to synthesizers by the time the DX7 hit.
And about the 909/303, back in the 80s/90s a lot of EDM tracks had 909 in the title, including a Daft Punk track. Same for some 303 tracks (but Acid was way more obscure). House and Techno people definitely heard about those. In fact, they were probably more popular than the DX7.
Sure none of those comes close to the 808 today, but that's because the 808 itself had a resurgence in the mid-2000s, and hip hop only got bigger since them.
Right up the top of this thread the first commenter explained it well: "The keyboard player's job moved from playing the piano or organ to coming up with all the accompaniment parts that aren't guitars."
What I don't know is if the DX7 itself was particularly recognized as a DX7 by most of the people listening to music that was made with it. My guess is that most casual listeners still just considered it "the thing that the keyboard player is playing". This is why I am not sure that it is as uniquely distinctive as the commenter near the top of this thread suggested.
Of course trained musicians can identify a DX7 in a track, just as they might be able to hear the difference between a Stratocaster and a Telecaster. Dedicated fans might also hear the difference, if they're interested enough to pay attention. But someone just listening to a tune on the radio, humming along to it, I don't think they're going to go "yep, that's the good ol' DX7 electric piano patch" or "yep that's a classic Strat sound".
Personally, I think laypeople do identify the 808 in this way, just judging from anecdotal conversations with people who are not musicians, not DJs, not "serious" music fans, just regular people. This is why I think the 808 is an interesting instrument, and perhaps special in a way that the DX7 wasn't, and the TB-303 and TR-909 weren't. That doesn't mean those other synths aren't special for their own reasons, I was just commenting on something I perceive to be unique about the 808 - a relatively widespread understanding of what its "sound" is.
If you are a hardcore music fan or a musician, it can be illuminating to do some testing with someone who isn't. Play them a song, point out some piece of equipment, explain to them why this song has a 909 hihat but that song has a 707 hihat, and how you can tell the difference. Then play them another song and see if they can identify the hihat. 9 times out of 10 that's not what people are listening for. That's not how they experience music, they don't break it down like that.
About 909s and 303s, like I said, they were special when they were in their heyday. Most people knew them by name, since there were lots of track titles, there was a TB-303 reference in Ghost in the Shell, and there are some TR-909 and TB-303 tattoos if you search Google... I'm not disputing that 808s are more famous now that hip hop is very mainstream, the 808 kick drum is in vogue for years and Kanye albums have 808s in their title. Like I said, you have to keep those things into context when making a comparison, otherwise only the 808 will ever count as "important"... that's it. Maybe the Moog is a better example?
On the 909/303, I don't dispute they were incredibly influential in the rave scene, especially in the 90s. I am one of those people with a 303 tattoo so I know very well what a reputation they had. But also I have some perspective on how small and dynamic that scene turned out to be in the greater scheme of things. Most of the ravers I know from back in the day couldn't pick a 303 in a song and don't even listen to acid or techno music any more.
I think a good comparison to an 808 is a Theremin. Lots of people, even people who don't listen to electronic music or hip-hop know the names of these instruments and can probably pick one out of a song. I'd see the 909 or 303 more like a Strat or a Tele - still very influential and recognizable to people who are interested, but perhaps not so much in the mainstream consciousness.
But this is all opinion just based on anecdotes, so I am open to the idea I might be overestimating the cultural impact of one bit of gear or the other.
At least in the U.S., lay people are notoriously bad at even knowing the names of instruments, much less pinpointing them in the overall musical texture.
About the only test you could do would be to, say, replace the Theremin in Good Vibrations with a string synth from the DX7. Most people have never heard of either instrument, but many would instantly recognize that something is off in that example. Probably the same if you replace a stratacaster, vocoder, etc., in a track they're familiar with, especially if you substitute it with something from a different historical period.
Other than that, I'm afraid all that's being measured is the effect of lack of funding on basic music education in the U.S. :)
For a polyphonic synth though it was a game-changer, it did make it affordable, but so did sh-101 and countless other synths but those weren't polyphonic. Roland Juno could be said, it wasn't revolutionary but more evolutionary in electronic music making. Here's a good article on DCO vs VCO https://blog.thea.codes/the-design-of-the-juno-dco/ and recent discussion here:
Actually even Aphex Twin is pretty famous... the only thing not famous is the phrase is the TR-606! hehe
Although there are loads of synthesizers that were extremely influential in the industry and are immediately recognizable to hardcore synth fans (M1, D-50, Prophet 5, TB-303, Minimoog etc), I doubt there are many that the average listener would consider to be "distinctive".
This is what makes the TR-808 special, I think, even though there are lots of other drum machines that can make the same sounds. It's become a part of the standard lexicon of hip-hop, R&B and electronic music. I imagine a fair amount of casual pop music fans know that when someone says an 808 beat is about to drop, they're gonna get that booming bass drum and typewriter snare, maybe a cowbell.
I'm not sure the DX7 ever had the same widespread name recognition, even back in its heyday. And outside of synths, I don't think the average person connects specific guitar models to distinct sounds either, even if they know the names in the abstract. The 808 might be unique in this. Then again, rock music fans might never even have heard of it?