As far as I know, some cables should not be disconnected from computer while it and/or the device is running and persistent hardware damage can occur if they are unplugged errorneously.
Currently the table is like this:
- USB, Firewire, Ethernet, HDMI - can connect and disconnect without caution;
- VGA Monitor - OK;
- Serial port (COM) - OK probably;
- SATA - should be more or less OK;
- IDE, PS/2 - not recommended;
- Parallel port (LPT) - very not recommended;
- CPU, RAM, PCI, motherboard to PSU slot, ... - I don't know.
I tried or seen hot disconnections for all mentioned above (expect of LPT and the last point) without any problems.
Why the slow or device can be damaged by sudden disconnection? What happens when some (not all) pins are not connected?
Does it still apply for ( LPT or PS/2 or IDE ) USB adapters? Can they also be damaged or "unplugged cable => burned port" is only for old legacy hardware?
Can a cable with damaged wires (but without any short circuits) damage the port or device?
Note: just software issues (data loss, operating system crash) is out of scope in this question. It's only about hardware failures that cannot be fixed without bying things.