The general thinking seems to be "it's MY money, so I should be allowed to write on it, tear it up or burn it as a protest against the banking system if I want to."
But in fact, it's technically illegal to deface U.S. currency to the point at which it's rendered unusable. The specific federal law at issue is 18 USC 333, which proscribes criminal penalties against anyone who "mutilates, cuts, defaces, disfigures, or perforates, or unites or cements together, or does any other thing to any bank bill, draft, note, or other evidence of debt issued by any national banking association, or Federal Reserve bank, or the Federal Reserve System, with intent to render such bank bill, draft, note, or other evidence of debt unfit to be reissued."
That's according to the federal Bureau of Engraving and Printing, or BEP, which quite literally makes money. (If you think the government doesn't have a sense of whimsy, consider the domain name of the BEP's website: >www.moneyfactory.gov.)
The law seems to suggest that defacement of currency that's minor in nature and doesn't render a bill unfit for use or that's accidental doesn't rise to the level of a punishable crime while deliberate mutilation, perforation and so on could be subject to criminal penalties. Note that this law applies specifically to bills. Coins are a separate issue.
The visceral reaction of "it's my money, so I can do whatever I want to it" might make more sense to me if money weren't by definition part of a system in which bills have value only because they can be circulated as part of the money supply. If we all adopted the "it's mine" mentality, money would be out of circulation, and a bill would be just a piece of fabric, 75 percent cotton and 25 percent linen. You could sew a bunch of those into a shirt, but you wouldn't be able to spend them.
So should defacement of currency be a crime? Or should it be OK to destroy money because it's "yours"?