Do I have to report income if the person who paid me doesn't file a W-2 or 1099?

Yes you do. The lack of a W-2 or 1099 is no excuse for not reporting income. IRS auditors routinely review bank statements and will assume all deposits to be taxable income unless you can prove otherwise.

Third-party payer information supplied to IRS, such as W-2s and 1099s, are means of allowing IRS to verify income received by payers. However, any income received by taxpayers, except for the few types that are statutorily exempt from taxation, are required to be reported as income.