The Cheese Tray
When I'm in the mood for a serious session of analytical wine-and-cheese tasting, I like to have a good array of cheeses and a selection of wines, tasting across the lines to compare and contrast the different ways they go together. But generally speaking, I'd propose the following broad categories for seeking the ideal marriage between a specific wine and a particular cheese:
Cheddars and similar sharp "English" cheeses: Dry reds, Cabernet Sauvignon or better Merlots.
Swiss, Gruyere, and the equivalent: Pinot Noir.
Blue cheeses: Sauternes (or other sweet, fine dessert wines) is traditional, but these also work nicely with dry reds, and surprisingly so with very dry (Fino) Sherries. Be careful about tannic reds like Cabernets, though, which sometimes get a funny metallic taste with blue cheese.
Ripe, creamy cheeses like Camembert and Brie: Rich, buttery Chardonnay. Or for a change of pace, try them with Champagne.
Hard cheeses like Parmigiano Reggiano, Romano, etc.: This is probably kind of a cliche, but I really do like them with dry Italian reds, from Chianti to Barolo. Or try a chunk of really fresh Reggiano with a heavy Amarone.
Dessert
Sweet wines are generally better sipped by themselves and not with food. There are a few traditional matches, including foie gras with Sauternes and other great dessert wines; Stilton (or other fine blue cheese) and walnuts with Port; and a creamy, not-too-sweet creme brulée with a fine dessert wine. But in my opinion it's best to have the dessert wine be the dessert rather than serving it with dessert, or save the dessert wine for contemplative sipping after the meal has ended.