What happens when my credit card does not work at a no-show?

It depends on a lot of things, but primarily the cancellation policy and how you booked the hotel room.

First the cancellation policy, I'm assuming you didn't pay money up front so the charge for a no-show is probably one nights stay (although it could be more). When you don't turn up the hotel will cancel your entire reservation, open the room for new reservations and attempt to take whatever the no-show charge is from your card.

Whether they succeed in getting money off your card depends on what they did when you booked (and why your card doesn't work).

Some hotels will just take your card number at the booking and not do anything with it. They may do a simple validation that it's a real, non-cancelled card or they may not. If this case the hotel has little option to get the money back. They will probably notify your card issuer, particularly if they have paper or electronic proof that you agreed to pay. What happens now depends on contracts with the card issuer but I think -- in general -- the hotel will not get the money but your issuer will put a note of the card records (and possibly your credit record) about the issue.

However many hotels, if they're not explicitly taking a payment up front, will pre-authorize an amount of money equal to at least the no-show fee. Here's a note about this from Wells Fargo:

An authorization is an approval on a cardholder account for a sale amount. An authorization hold is a reduction of the cardholder's credit line for the amount of the sale. This hold can remain on the cardholder's account for up to 30 days, depending upon the issuing bank policy.

When you're conducting a transaction and you need an authorization, remember that the authorization must be for the identical sale amount. If you receive an authorization for the wrong amount, delete the incorrect authorization, and re-authorize for the exact dollar amount. However, you can pre-authorize for a different amount than the sale amount if you're in any of these industries: car rental, hotel, mail/telephone order, or restaurant.

So the hotel can try and charge the card even if it no longer works, this means the closed account balance can be in arrears and the card issuer will try and claim the money back and will (eventually) mark your credit record.

In general, without knowing the hotel, it's difficult to say what would happen. In my opinion, Large hotel chains have more cash flow and can write off single no-shows but they also have more stuff and corporate offices who can chase people if they feel it's worth it. Small hotels are more likely to need the money, but less likely to be able to spend the effort required.

You don't say why your card doesn't work -- if it's just expired and been replaced that charges can carry over to the new card. If you explicitly cancelled it then you probably acknowledged something about still being responsible for charges not yet processed.

In general you're much safer trying to contact the hotel and let them know the situation. If they have sufficient time to get a new booking for the room they're unlikely to go after you for the money.

Technically, you have breached the contract any may also be guilt of theft, depending on the laws in the jurisdiction where the hotel is.

However, most of the time, the property will simply write it off since it's not worth pursuing.