My York Diamond 80 furnace is working and heating the house right now, but as it cycles off - just seconds before it shuts down - it makes a real loud knock. We can hear it from the basement while we are on the first floor.

Any thoughts on why that's happening and how I can fix it (and how long I can expect before it gets worse and doesn't come back on after a big knock?)?

First you have to determine what the knock is coming from, is it the gas valve as it turns off, or is it the blower wheel making a noise when the motor stops. It could be that you have a metal frame on your filter and it is being lifted while the blower is blowing and when the air slows down as the furnace cuts off the metal frame is dropping back into place and making a knock.

One other thing Can you describe this sound is, is it a sound like metal metal, is it a sound like a metal pie pan makes when you press the bottom. If it is this could be caused by the duct work expanding and contracting as the air pressure increases in the duct work.

There are many things that it could be, you just need to be the detective and search around when the furnace turns off. Actually you should be there by your furnace when it comes on and listen for any noises, like the metal in the furnace expanding. Try to determine exactly what the furnace is doing as the noise is heard.

If you find something let me know and if my opinion helped rate my answer.

Turn off the poiwer to your furnace.
Remove the blower access door.
Reach into the blower housing
Try to move the blower cage that is attached to the motor up and down and in and out. If it is real loose or the blower wheel is loose on the shaft of the motor you have found your problem. While you are at it check your air filter also.

If your blower is dirty like this one it will need to be pulled and cleaned then checked.

Attached is something similar to my furnace. The knock seems to come from the bottom of the stack. Not sure how much this helps. Just seems like the blower turns off and then two seconds later... THUD. Not metal on metal - no "metallic squink." Just a thud - possibly something more blunt on metal?

My first thought as well is to check the blower as hvac1000 has suggested.