Do you have to pay taxes on stocks given to you by company you work for?

Not as long as you still own the stocks. In the year that you sell them you and the IRS will receive a copy of a 1099-B with some of the information that you will need to report the transaction on the schedule D of the 1040 income tax return. You will either have short gains (held one year or less) or long term capital gains (held more than one year) in the year that they are sold.