When workers are paid "under the table" (often in cash), their boss is trying to avoid protections and rights that workers have. Without paperwork, bosses hope to hide that the worker is an employee. Workers who are paid "under the table" can protect themselves.
When workers are paid under the table, bosses don't pay social security taxes, unemployment insurance, or workers' compensation. It also means that they're not deducting taxes from the workers' pay or reporting the income to the government. (That may seem like a good thing, but it can be a problem later on.)
Workers still have the right to minimum wage and overtime and can file a complaint just like any other worker.
Keep track of your work hours (the Department of Labor has a booklet you can order for free -- the link is in the Resource Box on this page). You may decide to prove later on that you were working so you can collect unemployment payments, workers' compensation benefits, or unpaid wages.
You can file a wage claim if you're not paid for all the hours you work, you aren't paid overtime, or you aren't paid minimum wage.
If you just want to make your boss start deducting taxes, paying into your social security and unemployment, and protect yourself, you can report the business to the IRS, using the report of fraud (see the link in the Resource Box on this page) or call the IRS Fraud Hotline at 1-800-829-0433. You can report the fraud anonymously (without giving your name). One thing to consider is that the IRS may tell the workers that they owe for taxes that they didn't pay when their boss wasn't taking anything out of their pay.