Match the problem to the agency and the complaint gets read by someone who can act on it.
Banks, credit cards, loans, debt collection, credit reports → Consumer Financial Protection Bureau. Forwards to the company, which must respond, and publishes response data.
Scams, fraud, deceptive advertising, identity theft → Federal Trade Commission. Feeds a database law enforcement uses, though the FTC does not resolve individual disputes.
Anything local, or a business behaving badly in your state → your state attorney general. Many run mediation programs that recover money for individuals.
Vehicle safety defects → NHTSA. Complaints trigger investigations that lead to recalls.
Workplace pay → Department of Labor Wage and Hour Division. Discrimination → EEOC. Safety → OSHA.
Housing discrimination → HUD.
Airlines → Department of Transportation, which has real enforcement authority over refunds and is worth using when an airline stonewalls.
Mail problems, including fraud by mail → US Postal Inspection Service.
Insurance → your state insurance commissioner, which regulates insurers licensed in your state and handles claim disputes.
Utilities → your state public utility commission.
Writing one that works
Lead with what you want. Give dates, amounts, account numbers and the names of anyone you spoke to. Attach documents. Keep it to one page and leave the outrage out, because a factual complaint is easier to act on and harder to dismiss. Send the same complaint to the company at the same time, since regulator contact often unlocks a resolution the front line refused.