Final answer:
Hot-pluggable external hard drive cable connectors include eSATA and SAS, allowing connection and disconnection while the computer is running without damage.
Step-by-step explanation:
The external hard drive cable connectors that are hot-pluggable, meaning they can be connected and disconnected while the computer system is running without causing damage or data loss, are eSATA and SAS.
eSATA, or External Serial Advanced Technology Attachment, is designed for external connectivity. It allows users to plug in external hard drives while the computer is on efficiently and effectively.
SAS, or Serial Attached SCSI, is another interface also designed to be hot-pluggable. It is commonly used in enterprise environments, allowing for expansion and replacement of storage devices without the need to shut down the system first.