Make It Rain, But Don't Set Fire To It

So let's say that you've had a little incident with your money. Oh, say, you've thrown it in an industrial shredder. Not your fault, as you keep telling everyone. It was that damned Godzilla again. Yeah, that's it. Godzilla. However it happened, now you've got a bunch of shredded money. You're screwed, right?

Not necessarily. You still have the pieces of money, right? If you can piece them back together enough, they might still be usable as currency. Let's put it this way: you obviously wouldn't accept money if a guy came up to you and offered you a little tiny scrap of corner, but you might if someone offered you the entire bill minus the tiny scrap of corner. The question is basically, at what point does a bill stop being legal tender.

In the linked article, it notes that Taiwan's threshold is 75%: if you have 75% of the bill lashed together somehow, it can be used. We compile here today the requirements in various other countries.

Australia: 80% gets you full value. Less than 20% gets you nothing. Anything in between gets you an amount of money proportional to the amount of bill you have. So if you cut a $20 bill in half, you now effectively have two $10 bills. If you cut it into one three-quarter piece and one quarter piece, you have a $15 bill and a $5 bill.
Canada: Same rules as Australia.
China: The exact threshold couldn't be found, I do know they will at least replace a whole note, and if you bring in a pile that looks like this, they're likely not going to be able to help you. My best guess is they require the whole bill.
Eurozone: 51%, though you can present less provided you can prove the missing majority of the bill has been destroyed. If the portion was intentionally destroyed, though, you're SOL.
India: Seems to be at least half, with provisions for paying half-value on notes of 10 rupees or above.
Indonesia: I don't know about now, but back in 1950 bill-ripping was used as a method of redenomination... that made everybody poorer. On March 19, 1950, the Indonesian people were asked to tear their bills above 5 rupiah in half- the left side was valid at half-value and could be exchanged for new currency a month later, the right side was to be exchanged for bonds worth way less than half.
Kenya: 51%, with at least one complete serial number.
Mexico: No provisions. If it's torn, you're screwed. Merchants won't even take it as a tip.
New Zealand: In theory, 51%. In practice, each of the four denomination values on the bill is worth a quarter of the bill's value.
Nigeria: Good luck. Not only are banks rejecting torn notes outright, some are rejecting dirty notes too. Though they'll be happy to give you the dirty and torn notes that they won't take. Bank customers are needless to say rather displeased with this arrangement.
Peru: 51%, and at least one of the two serial numbers.
Philippines: 60%.
Singapore: Banks aren't obligated to give anything for any damage. They can if they want, but anyone that does is just being nice to you.
Taiwan: 75%.
Turkey: Over half the note in usable condition will get you the whole amount back. About half the note will get you half the amount back. Less than half gets you squat.
United Kingdom: 51%, or the parts with important things such as the serial numbers.
United States: 51%, though key parts of the bill need to be present and you are going to have to explain what in blazes happened to it. Also, present it as-is.

One thing that's true across the board is that pretty much nobody on the planet is going to accept any foreign bill that has even the slightest tear in it, and banks the world over love to pawn their torn bills on stupid foreigners who don't know any better. If you get torn money, you'll have to raise a big stink about it until they give you money people are more likely to take.