Do you have to pay a tax on stocks that were left to you?

No. You don't have to pay taxes on ANYTHING left to you. It's a gift, and the person (or estate) leaving it to you would have to pay any estate taxes.

Also, when you sell the stocks (for capital gains) you will only be taxed on the increase in value from what they were worth the day your benefactor died, something called the "stepped-up basis".