In 2001, a 22-year old American woman got her tongue pierced. It seemed to get infected almost immediately and appeared to be discharging pus. Within a few days she couldn't take the discomfort any more and removed the piercing (in hindsight, likely trapping the infection inside her tongue). Everything seemed fine, but four weeks later she started getting severe headaches, nausea, vomiting and dizziness. These got progressively worse and after two days she was admitted to the hospital where CT and MRI scans showed something in her cerebellum.
Brain surgery was performed to drain what turned out to be a large abscess, and after six weeks of antibiotic treatment she was fully recovered. A very similar case happened to Carla McPhie of Ajax, Canada, although her infection came 10 months after the piercing (and she had to have part of her skull removed afterwards).
Brain infections of this type are not unheard of, although they are rarely linked to piercings — more often they are an offshoot of ear or sinus infections. These ones were believed to be linked to the piercing because the bacteria in the brain was streptococcus viridans along with other bacteria typically found in plaque (i.e. an infection started in the mouth, became trapped inside the tongue, festered, moved through the bloodstream, and settled in the brain).
Brain infections are really not a serious risk of tongue piercings, any more than a piano falling on you is a serious risk on your afternoon stroll. That is, this type of infection is more so "freak accident" than something you should worry about. Assuming you don't do something silly like the first case and trap an infection in your body, the odds are slim-to-none that this will happen.
Anything that could cause an infection (papercuts, stubbing your toe, picking your nose with dirty fingernails, etc.) could lead to a brain infection just as easily as a tongue piercing.