You can do everything with valves or microrelays. But, without semiconductors you cannot do microprocessors. Miniaturization cannot take place so you wont see portable devices. You can integrate and miniaturize valves :
We cannot know how much more could thermionic valves be miniaturized or integrated. Transistors provided a easier path and that was followed instead.
With this in mind you can build the following:
- Digital and analog computers.
- Radios and TV.
- Limited cellphones (handheld radio transceivers)
- Analog circuitry.
Due to the lower reliability of valved circuits, you would not want to do:
- Eletronic engine controls. (You can control a engine with a valved analog circuit, but valves are too much sensible to vibration)
- Too complex life support systems.
You cannot do :
Decided to edit my post because of a lot of answers with wrong ideas being posted:
You can do computers with vacuum tubes (called valves in UK). The computers can be quite complex. The only difference between a modern computer and a computer made with vacuum tubes is scale. Transistors are made today on nanometer scale while the smallest valve could be made at milimeter scale. This means a lot of things.
1 - The less integration increases path delays amont units. This means that there will be a upper limit on the maximum speed of the computer. And this limit will be much smaller than the limit imposed on current silicon-on-sapphire designs. Integration means that all devices that compose a microprocessor are micrometers away at most.
2 - The use of a heat source to make thermionic emission possible means that valves have a much larger thermal footprint than semiconductors. This means that large designs will present a thermal management challenge.
3 - They use a lot more power than semiconductors.
This means that computers will tend to be centralized and used as a kind of utility, just like your phone, your water and your eletricity. What you would have at your home would be probably a dumb terminal made out of simple valved circuits. Multitasking at the central computer means that a lot of people can and do stay connected at the same time. Maybe the generally smaller bandwidth disponible will preclude the development of graphical applications. Etc. In other words, computers will gravitate mainframe era designs.
About modems, yes, you can do modems with vacuum tubes. What must be understood about vacuum tubes is that they have the behaviour of a cmos transistor. BUT, they operate at higher voltages and their size is much bigger than the usual CMOS transistor. This means that anything that can be done with CMOS transmistors might be possible using vacuum tubes, minus the miniaturization. You can do ASK/FSK/PSK modems with vacuum tubes. You can do analog to digital converters. etc. You can do precision guidance systems.
For one, the missiles and radar on the MiG-25 (and other aircraft of the era) where fully vacuum tube based. Guiding a missile across a radar beam is precision guidance (just not fire and forget, but its not all that hard to build radar homing active guidance missiles with vacuum tubes).
About TV. Analog color tv is designed around backward compatibility with analog BW tv. This placed certain constraints on the signal quality. Color information is carried in a phase modulation embedded into the luminance signal of the original BW tv. This means that a limited bandwidth was divided between two signals. Luminance gets most of the bandwidth. But, provided that there was no transistors disponible and people wanted a higher resolution TV standard, you can increase resolution by increasing the bandwidth disponible. This means that the usually 6mhz color tv channels used in analog NTSC tv might be enlarged to 12mhz or more to include a separated color carrier. This alone can increase the perceived resolution of color tvs. Thats not impossible, it was not economical at the time the color tv standards where created.
Regarding satellites, most satellites are operated as dumb repeaters. Eletronics inside the satellites are at premium. Space is constrained by thermal management needs and the general cost of launch that is proportional to weight. Being at 300km above ground or more means that repair on-site is impossible or quite costly (see hubble space telescope). This means that eletronics inside the satellites are bare, just enough to repeat signals. You can include beamforming systems on the sats to increase the bandwidth disponible by employing spatial multiplexing, and the algorithmns involved in such beamforming might very well be beyong vacuum tube capabilities, but, non-beamforming sats can be and are still usefull. So, miniaturized valves or not, you can still build satellites. A side not is about a computer capable of guiding the apollo missions. Yes, it can be done. Usually if you cannot treat some problem digitally you can do it in a analog computer. So, provided that you can miniaturize valves to 30mm scale, you can very well build a small computer capable of integrating speeds and other variables needed to space travel. You can beam a couple of tight radio wave beams towards the moon, you can do WW2 era navigation with radio navigation aids. You might be surprised what can be achieved with vacuum tube technology. You might be interested in the battle of beams wich ocurred in WW2. Collossus and other computers of the time might provide a hint how computers would evolve if vacuum tubes where the only option.