Do I pay tax on stocks if I never sell them?

Not on the gain itself. A stock that has tripled since you bought it has produced an "unrealised" gain, and unrealised gains are not taxed. You could hold it for forty years and never owe a cent on the appreciation. The tax is triggered only by selling, or by certain events like a cash buyout that count as a sale.

What you do pay each year is tax on dividends. If the company pays you $200 in dividends, that $200 is taxable income for the year, even if your broker automatically reinvested it. So a portfolio of dividend-paying stocks generates a small tax bill annually while a portfolio of non-dividend growth stocks generates none until you sell.

This is the logic behind "buy and hold" as a tax strategy. Every year you do not sell, the money that would have gone to taxes keeps compounding for you. And under current US law, if you hold until death, your heirs inherit the shares with the cost basis reset to the current value, and the gain is never taxed at all.

None of this applies inside an IRA or 401(k), where neither gains nor dividends are taxed while the money stays in the account.