What type of plug is this, and can I replace it?
That is a twist-lock-style plug used with receptacles like this:

Receptacles are still available - I have no idea if it's code-allowed to use them, they're not at all common in my experience.
I would also be inclined to replace the plug for use with a normal common socket. Check the electrical ratings on the equipment for how many volts and amps it uses. These twist-lock receptacles I found go from 120V/15A up to 220V/20A so what's safe and proper would depend on your device/appliance.