Belgium was a country in western Europe, a continent on Earth. This was an European Alliance member state. Cities included Brussels, Antwerp and Waterloo. This region, like Armenia, was identified by Captain James T. Kirk in 2267 as a vulnerable waypoint situated on the invasion routes of many invading armies in Earth's history. The flag of Belgium was three vertical bands of black, yellow, and red. (TOS: "Errand of Mercy"; ENT: "First Flight")
In the alternate timeline 20th century created by Vosk and the Na'kuhl, Vladimir Lenin was assassinated, and Adolf Hitler could focus on the West. He took France, then Belgium and the Netherlands quickly fell. (ENT: "Storm Front, Part II")
In 2143, the Ariane 1 assignment patch, which was on display in the 602 Club, bore the flag of ESA member Belgium. (ENT: "First Flight")
In 2325, Devinoni Ral was born here. (TNG: "The Price")
In 2372, Antwerp was targeted by the Dominion. A changeling infiltrator detonated an explosive device there. (DS9: "Homefront")