Unless the laws have changed, in the United States, you are required to report any affiliate earnings over $600 dollars with any one company. For example, if you earn $600 with Affiliate Network A and $500 with Affiliate Network B, you need only to report network A. Most networks will collect your tax information and even have you sign a W-9 form. I recommend you look into the specific tax laws for your government and state to be sure, and if you don't want to put yourself at risk, I further recommend that you file everything you're required to or sit down with a tax specialist at your local H&R Block or something.
However, it's extremely unlikely that the IRS would find you if you didn't report your online earnings. Just sayin'