There used to be a virus/trojan that would execute the floppy drive head re-calibration interrupt (BIOS) in an infinite loop to cause the head alignment to go out of whack, rendering the drive defunct.
CPU interrupts - handlers for CPU errors like division by zero (0h) or overflow (4h).
IRQ interrupts - handlers for hardware events; e.g. hardware timer (8h) or keyboard (9h).
BIOS interrupts - for BIOS-implemented syscalls; e.g. video output (10h) or sector-oriented disk I/O (13h). Also callbacks to be invoked by BIOS, like the aforementioned 1Ch for configurable timer.
DOS interrupts - for DOS-implemented syscalls; mostly this was 21h with actual syscall ID in the register. This is where you got things like file-oriented I/O, and some basic memory management.
And then there was "everything else", meaning things installed by third party TSRs and drivers. For example, 33h for the Microsoft mouse driver (which all other mouse drivers promptly copied, so it became the de facto standard mouse API in DOS), or 3Eh for Borland's software floating point emulator.
Of these, only the first two are actually "special" as far as hardware is concerned - the rest is just convention.