This little country produces a plethora of beer, but there are only two breweries within Brussels: 1) Cantillon and 2) Brasserie de la Senne. Cantillon has a great, cozy tasting room and tours of the brewery. Brasserie de la Senne is newer and I don't think it has a tasting room yet, but look for it in bars all over town. They are very proud to produce quality beer in the city - Brussels Calling!
My favorite Belgian beer is Tripel Karmeliet, which is brewed by family-owned Brouwerij Bosteels. The family, which totally won in grabbing a great domain name, also brews Kwak (very fun glass) and Deus.
Trappist beer carries an official Trappist label that ensures the beer is brewed in a monastery by servants of God who do not exploit the product for profit other than maintenance of the monastery. So you can be sure you're not getting some soulless monopolist's commercial crap. There are 6 monasteries in Belgium that produce certified trappist quality thirst quenchers: Westmalle, Rochefort, Westvleteren, Chimay, Orval, and Achel.
Abbey beer, on the other hand, is not necessarily related to an existing abbey and the name could be a commercial ploy.
Lambic beer is a wheat beer with some sort of special brewing process using ingredients native to the Brussels region so is best drunk vom fass.
Duvel Moortgat Brewery (Brouwerij Duvel Moortgat) is a Flemish family-controlled brewery founded in 1871 that sells Belgium's most popular blond ale. It's not a total sell-out, but it is a public company with at least part ownership in NY's Ommegang, MI's Boulevard, and fellow Belgian brewers Achouffe and De Koninck.