In some countries yes - as you are defacing the currency and won't be accepted. In the USA it is, but the laws are rarely enforced.
In Canada, it is illegal to hored money except in a bank, you can't keep it out of circulation. You cannot deface money because it is a legal document. No one really cares. In Canada and the states there is a fun game www.whereswilly.com and in the states theres a game called www.wheresgeorge.com. You can enter the serial number and track a bill.
AnswerTaken from The "wherehaveIbeen" website: This is, by far, the most commonly asked question we get and the answer is...
Not unless you're making them "unfit for recirculation" and, according to Title 18, Section 333 of the United States Code, this is defined as "mutilating, cutting, disfiguring, perforating, uniting or cementing together, or doing anything else to a bank bill
with the intent to render such item(s) unfit to be reissued". So, if you're only writing the "www.WhereHaveIBeen.com" website address in neat lettering along one edge of the bill, you're certainly not making it "unfit for recirculation"!
"Of course, that's the American side of things. What about in Canada?"
At this time, there is
nothing mentioned in either the Canadian
Bank Act or the Canadian
Criminal Code (see Part XII; Offences Relating to Currency) concerning the defacement of bank notes.
While the Bank of Canada (who decides whether a bill is to be removed from circulation and replaced) does not condone writing on bills, those bills remain legal tender and can be used in commercial transactions. For more information, please feel free to contact any member of the Bank Note Communication and Compliance Team of the Bank of Canada at 1.888.513.8212.