One factor determining whether you should use a vapor barrier for your brick garage is whether the garage is attached to your home. If the garage is attached and the dividing wall between the garage and the house has a heated room on the house side, you may at least need a vapor barrier there. This is especially true if you don't plan on keeping the garage the same temperature as the house. Any time you have the potential for warm and cold air meeting, you have the potential for condensation and need a vapor barrier. An unattached brick garage without a shared wall would not necessarily require a vapor barrier.
The purpose for which you use the garage also influences whether you need a vapor barrier. If, for instance, you use the garage as an office space or workshop, you may need to protect the valuable items inside by putting up a vapor barrier. This is especially true if you heat and cool the inside of the garage and subject the outside walls to potentially extreme high and low temperatures. Condensation and moisture build-up could destroy valuable paperwork or other equipment.
Even if you don't use the garage all that often or control the inside environment all that strictly, you may still want to install a vapor barrier if you plan to insulate the walls. You may not use the garage for anything but parking your cars, but should you insulate the walls in anticipation of a different use later, it's hard to install a vapor barrier once the insulation is already in place. Putting the vapor barrier in from the outset makes your life easier.
Where you live can also play a role in determining whether to use a vapor barrier. Danny Lipford notes that vapor barriers are most often used in cold climates, where the home is heated on the inside. With a brick garage, this goes back to the question of whether you intend to heat it. If not, you need a vapor barrier. In some geographic locations, such as the warm, humid areas of the U.S. Southeast, vapor barriers may not be advised on the inside because of the potential for a reverse effect from air-conditioning during the summer months, Lipford says.