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In 2002, you could buy a PC motherboard with a sound section amplified by a dual-triode vacuum tube. You can still find them on eBay: http://ixbtlabs.com/articles2/aopentube/
There's still a market for tube amps, although most are external for both aesthetic and practicality purposes.
Reminds me of the people who hook their Raspberry Pi up to a tube amp just to listen to Spotify.
If you search for “The Tube Guys”, the front cover of that book shows a 94 GHz, 1 MW tube used for an airborne active denial system.

Traveling Wave tubes are still widely used for SATCOM.

Other than ADS systems, and the audio and microwave ovens mentioned in the article:

- Huge-ass klystrons used to drive particle accelerators (which themselves can be thought of as the largest vacuum tubes ever made)

- High-power transmitting tubes used in radio and TV broadcasting

- TWTs are still used for some satellite communication work, both on the ground and onboard the space vehicles

- There's still no solid-state substitute for X-ray tubes. Hard to find a semiconductor with a 50,000-volt band gap

- Cesium-beam tubes used for timekeeping (as well as masers used for the same purpose, for that matter), although entire atoms are emitted in those sorts of tubes rather than just electrons

If you don't count fluorescent lamps as "vacuum tubes," those are about all the remaining applications I can think of.

High power RF transmitters are still a notable realm of tubes.
In the microwave frequency range for TWTAs but not so much at lower frequencies. I worked with MRI amplifiers for a while (64 MHz or 128 MHz, depending on 1.5 T or 3 T) and things have gone solid state there. Broadcast seems to have followed the same path.
The article briefly mentions magnetrons and X-ray tubes, the former of which is made in massive quantities today for consumer appliances. Other vacuum tubes in current use include the vacuum fluorescent display, the photomultiplier tube and the electron multiplier tube. I believe old school vacuum tubes also still have application in high-wattage class-C RF power amps. Vacuum tubes for audio receive a lot of lip service, but they really are botique, lunatic fringe stuff in that application. Magnetron tubes are the only practical choice for microwave ovens; in contrast, power output tubes for audio amplifiers are inferior to semiconductors in every way.
What this article doesn't mention is why vacuum tubes are still used in guitar amplifiers:

The "distorted guitar" sound common in rock music is a direct result of nonlinear characteristics of tube amps (both the tubes themselves and the coupling transformers necessary to connect an output tube to a speaker). Tubes exhibit "soft clipping" when pushed to their limits, which has the effect of producing the harmonic content associated with distorted electric guitar. Rock and roll pioneers got their sound principally from driving tube amps past their limits. "Overdrive" pedals are usually just voltage boosters that make the amp's input signal louder, but this pushes the amplifier past its clean linear section into the nonlinear crunchy overdrive that guitar players want.

Modern tube guitar amplifiers, even "new" designs, generally follow one a handful of basic circuit topologies, all derived from a few classic designs. Even the iconic Marshall "Plexi" amp was a close copy of an earlier Fender. These circuits are extremely simple; a handful of tubes, transformers, and passive components, often less complicated than the internals of a single LM741. Here's an example: https://www.thetubestore.com/lib/thetubestore/schematics/Fen...

It's possible to mostly recreate this sound with digital signal processing or carefully-tuned solid-state analog circuitry, but players like the sound of tube amps and are willing to pay for them, and so the market exists as it does.

Capacitors are also important:

http://www.gibson.com/News-Lifestyle/Features/en-us/3-Classi...

Some old leaky "bumblebee" capacitor is worth $75 if it happens to be the .022 uF value found in certain guitar tone control circuits.

One of the main source of innovation in guitar amps (aside from bells and whistles like alternate channels and effect loops) are typically the "tone stack", i.e. the capacitance of the tone control caps and their position relative to the power and pre-amp tubes in the circuit. The amplifier circuits themselves are mostly taken from RCA radio amps dating to the 1930s and licensed by Fender in the 50s.
I’ve found that a really good proxy for how good an amp sounds is the number of line-items in he BOM. The fewer the better.

A lot of the classic designs that sound good and still sell have exactly what they need to get the job done well and no more. It’s almost like all the major (and boutique) amp manufacturers took one of three or so amp designs and just threw components at the schematic until you couldn’t recognize it right away, and sell it as some revolutionary design. I wouldn’t be surprised to find that it it all came from some RCA reference design in 1950

There some truth to that, but not always.

Ideally you would want each time to be fed with a noise free constant current supply. Having each tube on its own power supply would be incredibly expensive but sound awesome.

Buffering the output of each tube would prevent blocking Distortion, but would also be fairly expensive (although now we have mosfets that can handle 500+, so that might not be as bad).

Split audio path about, where the bass goes through cleanly and the treble is overdriven would also sound incredible, but be expensive.

Designs end up being about compromise: the above features will add $5-$35 to the bom per tube, and in the end, a lot of people just end up buying on brand.

My Laney Lionheart L5T has a really cool preamp that uses solid state surface mount components where they don't affect the signal. This drives the bom cost down but sounds incredible (fully buffered fx loop, fully buffered reverb tank).

And further counterpoint: some guitar players like the sound of overdriving a tube power supply (the attack on a loud note reaches current limits for the p/s rectifier tube, dropping rail voltage, increasing harmonic content). Mesa "dual rectifier" amps made this an option, letting players switch between tube and solid-state rectifiers.

There's definitely room for "improving" guitar amplifiers; I personally think that many guitar players like classic sounds, buy on brand as you said, and the brands just try to reproduce classic designs with any deviations made for cost more than for any other reason.

Don't forget that transistors have a different and more loud background noise that vacuum tubes. I don't appreciate the difference but I know that some people could notice and appreciate the different kind of noise.
This is a great example of "worse is better". Unlike amplifiers made for listening to music, in a guitar amp you want that distortion and non-linearity, you want it to be wild and resonant and you want it to be sensitive to what you do on the input side.

Not directly related to tubes, but see the enduring legacy and popularity of the Boss HM-2 distortion pedal in metal circles, very often employed with all the knobs turned to eleven for maximum crunch. It was used to great effect primarily by Swedish death metal bands such as Dismember, Entombed, At the Gates and their compatriots. The tone is rough and textured and just feels right for the genre, so much so that it is considered a clearly defining characteristic of that particular branch of death metal.

Just like tube amps, it's preferred because it's imperfect in just the right ways to produce an artistic result.

Glad I have not jettisoned the two or three boxes of tubes stored up in our water tank tower that I inherited from my father in law - Time to go exploring again!
Photomultiplier tubes, still pretty much the only solution for photon-counting applications.
I recently designed and built my own guitar amp. I highly recommended the book "Designing Preamps for guitar and bass". Absolutely fascinating read and software engineers could learn a lot from the writing style! It's very approachable.