Is wiring money illegal under any circumstances?

Wiring money is legal. However, it is illegal to wire money if you are engaged in a business or activity for which you might need to be licensed, or registered and regulated. This is especially true for handling 3rd party funds.

For example, if you do any activity as a business and engage in such a manner so as to become a financial intermediary or say a cross-border payments facilitator (but still an intermediary), then the act of wiring money without a license is illegal.

Just to clarify, the act will be illegal, not the actual wiring itself.