I just read a very long and, frankly, disturbing Facebook conversation about sales tax when a military member buys a vehicle. The disturbing part was how much misinformation was included in this conversation, which is impressive considering that the basic answer is "it depends on your state."
Military members must pay sales tax on purchases, just like everyone else. What gets a little tricky is that the sales tax is based on and paid to the state in which the car is registered, which is often different from the state where the car was purchased. In addition, some states have lower rates or special deals for active duty military. There are also a variety of different ways that the paperwork can be handled.
If you're buying from a company, aka dealership, you will have to make sure that they understand that you are registering the car in a different state. Some dealerships will want to charge you the sales tax and handle your titling and vehicle registration, while other dealerships may let you handle that paperwork on your own. If the dealership insists on doing it for you, or taking out sales tax for the state in which the vehicle is being purchased, be sure to get very good paperwork and receipts. (For the record, I always push them to let me do it. That way, if it gets messed up, it is my fault.)
If you are buying from a private individual, you will be responsible for making sure that the correct paperwork is filed and that the proper taxes are paid.
I have found that the motor vehicle people, whatever they are called in your state, are usually very helpful. Occasionally, I'll get a clerk who just doesn't get the military, but that is rare. If that happens, I just call back later or try a different office. I've never gotten completely stuck.
All these rules apply to both new and used car purchases, and vehicles purchased overseas being brought into the US for the first time.
Next time you purchase a car, familiarize yourself with the sales tax and registration rules for the state in which you plan to title and register the car, and check out any special breaks for active duty military. Please don't get your information from your buddy, who may have a car registered in a different state with different rules, or from Facebook, where there are apparently a lot of people who don't understand. Each state is different, and you need to know the right information for your specific situation.