This happened to us a few times. Credit card companies can be very fickle things, they allowed someone that wasn't us to pay for $500 worth of CDs across the world, but blocked a local hotel we were staying at from finalizing the charge for our room.
When we travel, we generally only bring one credit card to minimize the potential pain of losing our stuff, and to minimize impulse purchases. We bring enough cash to fit our budget for the trip, and generally don't bring bank cards as well. We try to travel cheap so our budget goes mostly for enjoying ourselves rather than the room we only spend a few hours a day in - but we try to stick with reputable, well known hotels. We don't always stay at a franchise, but we do make sure the place we're staying is some sort of an established landmark in the area that we'll be traveling.
This sort of thing happens a lot, and hotels are quite used to dealing with it. Generally, as long as you promise to pay and have provided working contact information for the hotel to reach you there won't be much of a problem. You just have to make sure you follow up with an alternate payment method once you reach home, or straighten out whatever mess was blocking it to begin with.
Now, if you run up a $1500 room service bill complete with cucumber facials and pedicures and suddenly find yourself without the means to pay for it, you'll probably meet a bit more skepticism from the hotel. Depending on the part of the world you're in, they may ask you to leave some kind of collateral that will be returned once the bill is settled, and they may involve the authorities if they feel that you were in fact trying to 'weasel out' of the bill - just like a restaurant owner might react if you could not pay for your dinner. There's no blanket answer to those situations other than be as reasonable and cooperative as you can to the extent that you feel is reasonable.
Never surrender your passport as collateral for anything, most passports have this printed right on them. That is a vital document that guarantees your safe passage through ports and it should never be given to a third party to hold. Most reputable hotels will be comfortable knowing that they can reach you after you've left and that you'll settle the bill once you have access to your resources. If they won't budge from their desire to have you leave something that would be at least inconvenient to replace if the bill wasn't settled, then use something other than your passport.
Another thing you can do is leave the credit cards you did not bring with a trusted friend or relative - and call them if you absolutely must have the numbers and expiration date for an emergency (I have a few of mine memorized, just from paying bills online).
The final scenario (this has happened to me) is the hotel suddenly not being able to process your payment due to a glitch on their end, and asking if you can settle the bill using cash instead. When this happened, I politely said that I expected to be able to settle my bill using my credit card and did not make alternate arrangements, the problem was their own but I'd be happy to send payment in another way once I returned home. The problem was magically resolved a few minutes later, so one wonders if they weren't just seeing if they could save on the credit card processing fee - something to watch out for at smaller 'mom and pop' resorts.