The answer depends upon whether the sale of goods itself is taxable. According to the Texas Administrative Code, Title 34, Part 1, Chapter 3, Subchapter O, Rule §3.303, Transportation and Delivery Charges:
(a) Transportation charges for taxable items. The sales tax applies to all transportation or delivery charges to a customer when a taxable item is sold, leased or rented on or after October 1, 1987, and delivery charges are billed by the seller or lessor to the purchaser or lessee. The charges for transportation or delivery, both before and after the sale, are taxable even if stated separately from the sales price of a taxable item. These charges are considered to be services or expenses connected to the sale.
The regulation is located here.
If you have specific questions concerning the taxability of specific types of goods, I recommend you call the Texas Comptroller's Office sales tax help line at 800-252-5555.