I used the plastic carpet protector across the doorways where my last two used to do this if I shut the door on them. Cut it to fit to the shape of the door frame etc as exactly as you can, and extend it a bit beyond each side of the door frame, both sides of the door. Fix it down with self adhesive velcro so that the hooky bit grabs the carpet.
Any idea how to stop them scratching the carpet everywhere else though? I have one who's blind and I don't want to make the place too scary and hostile for him (eg smelling of citrus and/or sticky tape on the floor) but both he and his sighted companion are wreaking havoc. They've only just started doing this in the last month or so - had them for 1 year, aged 9 and 11 years.