Type a number in any base from 2 to 36 and see it in all the common ones at once, with the binary laid out in bytes so the bit pattern is actually readable. Useful for reading flags and masks, debugging colour values, and anywhere a hex dump needs decoding.
Because one hex digit maps to exactly four bits, so a byte is always two digits and the conversion is mechanical. Decimal has no such alignment - 255 gives no hint that it is eight set bits, while 0xFF makes it obvious at a glance.
They mark the base in source code: 0x for hexadecimal, 0b for binary, 0o for octal. A leading zero alone meant octal in C and several older languages, which is a famous source of bugs - 010 is 8, not 10. Modern languages require the explicit 0o.
Mainly Unix file permissions, where three bits map neatly to one octal digit: chmod 755 is rwxr-xr-x. Outside that it has largely been replaced by hexadecimal.