If you drive to Alaska, first remember you will have to go through Canada to get here. Therefore, it is a good idea to bring a passport if you have one. If you do not, picture ID and a birth certificate will suffice.
Also remember that it is a long drive and you should be prepared with all of the safety equipment necessary for an extended road trip.
If you plan to bring your pet along, be sure to get a certificate of health from your veterinarian.
For more information, visit the Department of Homeland Security's page on Crossing the U.S. Border for more details. Also visit the Travel to Alaska by Road on this site.