It is absolutely true that most of the jobs for which vacuum tubes (or "valves", if you're a Brit) were used, as late as the 1960's, have been taken over by semiconductors. There are excellent reasons for this. Vacuum tubes are inefficient. They are bulky. In most applications they are far less reliable than semiconductors. Generally, we're better off without them.
However, they've managed to hang on in several areas, and the technology upon which they are based is valuable for many industrial and scientific processes that are unlikely to be replaced any time soon.
You may very well be reading this website using a vacuum tube, a CRT (Cathode Ray Tube). While this application, too, can be replaced by a more compact flat-screen technology, the new display types are not quite competitive with the good old CRT for desktop PCs. Yet! While I look forward to the day when I can trot out to Circuit City and buy a flat-screen HDTV unit for under half a kilobuck, every TV I presently own uses a CRT.
In your home and office, you probably have a microwave oven or two. The key component of these wonderful appliances is a vacuum tube called a "magnetron". This is essentially an old-fashioned diode, with an electron emitter (cathode) and an anode target, with a magnetic field and a tuned cavity system.
A few audiophiles cling to the notion that vacuum tubes have a noticably "sweeter" sound than can be achieved with semiconductors.
Vacuum tubes have one instrumentation niche in which they are clearly superior: extremely high-impedance measurements. There are semiconductors with very high impedance inputs, JFET and MOSFET transistors, or integrated circuits based on them. However, the semiconductors are not tolerant of high voltage. I own a Keithley 610B electrometer (a hyper-sensitive meter capable of measuring current in the nanoamp range or measuring voltages from sources incapable of producing sufficient current to achieve a reading on most voltmeters). I prefer the 610B to the all-solid-state 610C. The B model is mostly solid-state, but has a nuvistor, a miniature vacuum tube, as the input stage. The FET-input 610C model can be blown by a tiny static charge on the instrument input, but the 610B simply shrugs off such an insult. In this case, a vacuum tube is far more reliable than a transistor!
Another scientific application for vacuum tubes is the ionization gage, a device for measuring high to ultra-high vacuum. This device is basically a plain old diode. The first instinct, upon seeing one of these happily glowing on a vacuum system, is to expect that the filament is going to cause trouble. There is, in fact, an alternative device, the cold cathode gage. Technically the cold cathode gage is still a vacuum tube, an "inverse magnetron," although it uses a small radioactive disk to produce the few electrons needed to get it running, and has no hot cathode. In practice, I've had one old ionization gage, bought used, run trouble-free for years, even tolerating a few boo-boos that caused the vacuum to fail. It has migrated to several experiments, and outlived its original solid-state controller. And, on that same apparatus, a cold cathode gage has needed teardowns for maintenance several times over the same period. The cold cathode gage also stops working at very low pressures, where the rate of ionization is too low to keep it running reliably. The ionization gage's steady flow of electrons keeps it running to far lower pressures.
Vacuum tubes are not yet dead in the radio transmission business, either, especially as you get into microwave power applications. The physics of generating microwaves, especially at extreme frequencies, does not always lend itself to transistors. I already mentioned magnetron tubes, and they continue to have applications other than kitchen appliances. Traveling Wave Tubes (TWTs) and Klystrons are also still in use.
Although silicon controlled rectifiers, thyristors, and Insulated Gate Bipolar Transistors (IGBT's) have replaced tubes in most switching applications, the old thyratron tubes continue to have a niche.
X-ray tubes are essentially high-voltage diodes with anodes made of metals selected for their x-ray emissions. Unless someone comes up with an X-ray version of an LED, this is another niche where the vacuum tube is secure.
The most sensitive light-measurement system known is the Photo-Multiplier Tube, or PMT. These use a photocathode to convert photons to electrons, with very high quantum efficiency. A photon in the visible light range will reliably produce a few electrons with a known probability. Each electron is accelerated toward an intermediate electrode called a "dynode", where it strikes, producing a number of secondaries (the more voltage between dynodes, the more electrons). The dynode string, or "electron multiplier", may have as many as 11 stages. PMT's can be set to such high sensitivity that they can literally count individual photons! Solid state CCD technology is marvelously sensitive, but not yet that good. Used without the photocathode, a bare electron multiplier can be used as a hyper-sensitive electron or ion detector. PMT's and electron multipliers are blazingly fast-responding devices. CCDs work by periodic scanning to determine the amount of discharge they have experienced due to photon impact, and this "integration time" must be fairly long at low light levels.
The things that happen in a vacuum tube are profoundly different than what happens in a solid-state device. A typical electron tube has an electron emitter (an incandescent filament or an indirectly-heated cathode). This component uses heat to "boil" electrons off of its surface. Nearby, an anode is placed, made positive with respect to the cathode, and the negative electrons are attracted to it. Various grids and other structures are placed between these parts to manipulate the electron flow.
Certain of these elements are vital in processes used in science and industry, and there is no way to substitute for them in solid-state. The key is the fact that vacuum tubes put a stream of electrons thru a vacuum or highly rarified gas. Electron beams are tremendously useful.
The same technology that produces a thin, focused beam of electrons in the CRT of your computer or television set is also the key to electron microscopes. Both Transmission Electron Microscopes and Scanning Electron Microscopes use such beams.
I mentioned x-ray tubes above. When electrons strike elements with sufficient energy, they cause transitions in the energy states of the electron orbitals of those atoms. As the electrons relax back to their preferred state, they emit the excess energy in the form of electromagnetic radiation. This can be light, but it also can be x-rays. Since a scanning electron microscope hits the item being imaged with a beam of high-energy electrons, a byproduct is x-rays. The spectrum of the x-rays can be used to identify the element being scanned, and can even allow an image to be produced showing the distribution of the elements present on a microscopic scale! No transistor will ever do this. A Scanning Electron Microscope (SEM) equipped to do this with an Energy Dispersive Spectrometer is called an SEM EDS system.
I mentioned ion gages above. An electron beam passing thru a rarefied gas produces ions. This property is vital to many scientific instruments, including mass spectrometers. Electron beams are bent by electrostatic and magnetic fields, and so can measure those fields. Electrons striking rarefied gas molecules undergo scattering, a measure of density.
Closely related to the x-ray production process is the emission of secondary electrons called Auger (oh-JAY) electrons, also of characteristic energies. Auger electron spectrometers also use electron beams, and have similar uses to the SEM EDS instruments.
Electron beams are also vital for many industrial processes. A powerful flood of electrons can melt bulk materials, even materials which cannot be melted in air. The temperatures achievable can melt even the most stubborn metals, such as tungsten, and the vacuum prevents oxidation and contamination. Sputtering occurs when electrons bombard a target made from a material you wish to deposit in a thin film on a substrate. The electrons boil material off of the target, and the material deposits on the desired substrate, perhaps with a bit of electrostatic encouragement. In fact, the semiconductor industry relies on these processes quite heavily!
While there are solid-state lasers, many of the most powerful lasers are gas lasers, and many of those designs rely on electron emitters.
Finally, some of the most high-tech R&D programs in the plasma physics world are basically just really big vacuum tubes.
I spent several years working on a nuclear fusion reactor concept which is, in fact, a direct result of vacuum tube technology. A quasi-spherical ion accelerator, it traces its roots to a spherical vacuum tube design dating back to 1924.
While I am a big proponent of electrostatic fusion, and believe it is the ultimate answer to the world's energy needs and the best power source for interplanetary spaceflight, the government has been working on other alternative approaches to producing fusion. Tokamaks are the "big dog" on this particular block. These devices rely on electron emission and beams, and on high-powered microwaves produced by vacuum tubes, for much of their basic function. The other approach is "beam-fired" fusion, either using lasers (again, some of which use vacuum tube components) or particle beams (either electron beams or ion beams, and the ions are usually produced with electron beams).
So, you see, the hoary old vacuum tube is far from dead. The basic physics of the vacuum tube are fundamentally different from solid state electronic devices, and it does some things no transistor will ever do.