Why do 1 pF capacitors exist?

The smallest capacitor I've used recently, in a filter in a 6 GHz receiver, was 0.5 pF. There were some 2 nH inductors there as well, and you could argue that those could be made with a few mm of track. However, both were smaller than the equivalent way of implementing them in copper.

Perhaps more importantly than the size, is that they were discrete components. When I wanted to change the capacitor from 0.4 pF to 0.5 pF, to retune the filter, I didn't need to respin the board; I just changed the bill of materials.

I use a 0.8 pF capacitor in a photodiode transimpedance amplifier (TIA) across the feedback resistor to reduce op-amp noise gain and I've used select on test capacitors from 0.5 pF upwards to centralize a 400 MHz colpitts based VCO.

I've also used a 1 pF capacitor in a quadrature FM detector for driving the tank so that I get high Q and the necessary phase shift of 90 degrees.

You'll also find them in RFID reader antenna matching circuits.

Here a good impedance matching between the transmitter and the antenna is essential for good performance, and you'll usually do the fine tuning with capacitors.

A 1 pF mismatch can easily make a 20% output power and thus reading-distance difference.

You don't use 1 pF or smaller capacitors alone. They're usually used in parallel with a bigger capacitor. So if your circuit calls for a 19 pF capacitor somewhere you'll use 18 pF and 1 pF in parallel.

Why not use 10 pF and 9.1 pF in parallel you may ask: The reason is, that it's hard to find 1% tolerance capacitors below 10 pF. Small values come with an absolute tolerance of - let's say - +/- 0.3 pF.

You get a better overall precision if you use a precision 18 pF part in parallel with a not-so-good 1 pF cap.