One peculiar little detail I found in a book about traditional Belgian cooking was that as many pages were devoted to beer as to wine. Belgian beer culture is truly special, and thanks Maastricht's location, it shows here as well. Of course, other countries also have elaborate traditions of brewing, and Dutch brands like Gulpener and Brand are both produced close to Maasticht. But I found that quite often, people stick to 'their' regional beer. In Belgium, however, the focus lies less on the origin but on the type of beer, every beer has its specific purpose. Thus, you don't always drink the same brand, but rather select the beer which is most appropriate for the situation or the meal you are having, very much like wine. For example, a fruit based beer is good for aperitif or dessert and a normal pilsener or a lambic fits well to light meals and mild cheese. Heavy beers like Abdijbier or Trappistenbier go better with hearty meals or strong cheese, but can be nice for dessert as well. By the way, the main difference between Trappist and Abdij (abbey) is that the former are brewed by monks, while the later are often only named after a monastery. Of course, this does not say anything about which tastes better.
In the end, you will have a try and find out which beer you like best. Due to the overwhelming variety of brands, a challenging but I'd say also a quite pleasant task. Most of the uncommon beers taste much better if you drink them at the right temperature and from the appropriate glass, thus it's best to explore the world of beers at a pub, even though most local shops have a good selection as well. To name only two of the many possibilities in Maastricht, the Take One in the Rechtstraat is famous for it's impressive assortment. If that's too much for you, the Café 't Pothuiske next to the river offers beer menus, courses of three or four different beers which fit well together.
If you are up for some experiments you might decide to brew your own beer. In Aubel, a small Belgian town just across the border, there is a shop which sells not only a wide range of local beverages, but also all the equipment and material you need to make your own beer or wine. It's a beautiful town with a nice market every Sunday morning, a jolly jaunt for a nice summer day, whether you are fond of Belgian beer or not.