Why do we use 32.768 kHz crystals in most circuits?
The frequency of a real time clock varies with the application. The frequency 32768 Hz (32.768 KHz) is commonly used, because it is a power of 2 (215) value. And, you can get a precise 1 second period (1 Hz frequency) by using a 15 stage binary counter.
Practically, in majority of the applications, particularly digital, the current consumption has to be as low as possible to preserve battery life. So, this frequency is selected as a best compromise between low frequency and convenient manufacture with market availability and real estate in term of physical dimensions while designing board, where low frequency generally means the quartz is physically bigger.
The number 32768 is a power of 2, i.e. it is 2^15. If you have a 32.768kHz clock frequency it is easy to divide it to an 1Hz frequency using binary frequency dividers, a.k.a. binary counters, i.e. chains of flip-flops.
Having a 1Hz frequency means you have a clock signal which provides 1s time resolution: count the seconds with a counter, do the math and you have a Real-Time Clock (RTC).
It's primarily due to cost. These particular crystals are dirt cheap due to the watch industry. This answer provides more detail, here's an excerpt:
There are 1.2 billion watches sold each year. The majority of them are inexpensive digital watches, requiring a small, 32kHz crystal. ...
As a result, these crystals are extraordinarily inexpensive... [Other crystals] cost 10 to 100 times more in quantity than these inexpensive watch crystals.
Further, these crystals are particularly well optimized for low power. Real time clocks are expected to run such an oscillator for 10 years on a CR2032 type cell. To get low frequency, low power, small crystals in other frequencies, you're looking at a substantial increase in cost.
In low volumes these crystals are still less expensive than even the normal or high power the 25kHz or 56kHz crystals, but cost the difference isn't large until you get into high volume manufacturing.
Choose what you need, but if you are going to produce a high volume product and can adjust your design to work with a 32kHz crystal, then there's a substantial financial incentive to do so.