Most STM32 have a 96-bit UniqueID, programmed in factory into in the system ROM. To explain, what the "uniqueness" of this number means, ST is saying this:

The 96-bit unique device identifier provides a reference number which is unique for any device and in any context.

While bold, this is not very specific. Nevertheless, the UniqueID is surely unique within specimens of the same STM32 model, and most probably unique amongst all STM32, too.

However, not all STM32 do have the UniqueID. This is especially true for the Value-line devices, i.e. those STM32 for which the base device number ends with 0 (i.e. STM32xxx0). The Reference Manual for these devices then does not contain the Unique device ID register (96 bits) subchapter of Device electronic signature chapter.

Some of these devices, confirmed by ST not to have UniqueID available, are for example STM32F070 and STM32F030.

Note, that this does not mean, that these devices may not have some data stored at addresses which are expected to hold the UniqueID in analogous devices of the same family. Rather, the number not guaranteed to be there or to be unique.

This is one of the drawbacks of using these cheaper devices, and an unpleasant surprise for those who wish to move from "standard" to value-line devices.