TODAY, in the world of C++ on x86 processors, it is pretty safe to rely on one byte being 8 bits. Processors where the word size is not a power of 2 (8, 16, 32, 64) are very uncommon.
IT WAS NOT ALWAYS SO.
The Control Data 6600 (and its brothers) Central Processor used a 60-bit word, and could only address a word at a time. In one sense, a "byte" on a CDC 6600 was 60 bits.
The DEC-10 byte pointer hardware worked with arbitrary-size bytes. The byte pointer included the byte size in bits. I don't remember whether bytes could span word boundaries; I think they couldn't, which meant that you'd have a few waste bits per word if the byte size was not 3, 4, 9, or 18 bits. (The DEC-10 used a 36-bit word.)