Do I need to pay the use tax on streaming services such as Netflix and Spotify?

No

A use tax is generally a non-recurring tax that is complementary to a sales tax.  Sellers of goods are required to collect and remit sales and use taxes to their respective State Comptroller's office or similar government entity responsible for collecting taxes.  While each State is different as to the amount of a use tax to impose, when to impose it, and which party to a transaction may be required to remit such tax, here is an example from the Texas Comptroller's website of how a use tax is applied:

"For example, you live in a city that imposes a 2 percent local tax. You travel to an area with no local tax imposed and buy a coffee table for $200 to use in your home. The seller only collects the state sales tax rate of 6.25 percent on the purchase. When you bring the coffee table back to your home, you owe the additional 2 percent local use tax of $4."

The above quoted material is just an example of a use tax.  Your particular situation may be different, and will depend in large part on where you live and where you conduct business.  Follow-up with any additional information; however, if you do, do not include any personal identifiable information. 

Here is the link to the Texas Comptroller website page that addresses the Texas Use Tax.  

Texas Comptroller