Soft-bodied, creamy, and a little salty, this cheeses works very well with a nice sparkling wine like Moscato d'Asti or a calm, yet equally sophisticated Moscato. Heavier wine possibilities include Cabernet Sauvignon, Pinot Noir, or Chardonnay. A Pinot Gris is also a brilliant choice, as long as it is fruity and not too sharp. A Riesling is also perfect, as is a Loire valley Chening. There are many great choices out there - the fun is in finding one that works!
Just remember that wine and cheese matches can be based either on similarity or on contrast. You can achieve balance by pairing similar flavors (tangy, acidic cheese with a crisp, tart wine), or you can combine contrasting elements (a pungent cheese with rich, sweet wine).
If you're a beer drinker, Brie pairs well with lagers, pilsners, pale ales, porters, and fruit ales (almost all of them). Sample Brie with a Belgian lager like Stella Artois, or a hoppy American microbrew IPA such as Victory's Hop Devil or Green Flash's IPA. The creamy Brie even goes well with a crisp, hard apple or pear cider. Enjoy!