What to drink is, obviously, an important question in my life. With cheese, the obvious, go-to alcoholic beverage is wine. The pair of foodstuffs is so linked semiotically that you're probably not allowed to use "cheese" as a clue for "wine" in Taboo. But wine is tricky, and sometimes you get a pairing that, like misaligned soundwaves, is destructive, rather than additive.
Since it's a lot of work to pair a cheese with wine, I tend to reach for other beverages when I pull out the cheese plate. There are a number of other, less finicky options that can pair just as well, if not better, with your fermented cheese of choice.
Beer, of course, is a classic pairing for farmhouse cheddars and other British cheeses, but the amazing range of beers available today makes beer a more versatile pairer than you might imagine. English-style bitters and porters pair well with strong, assertive cheeses like cheddars, cheshires, and caerphilly, while Belgian ales and French farmhouse styles, with their restrained sweetness and meaty savoriness, are a natural pairing to Alpine styles like Beaufort, Comte, or Gruyere. California IPAs, with floral notes and a resiny backbone, have a natural affinity for goat cheeses, which bring lemon and green peppercorn notes of their own to the table. Try pairing a sweet, strong beer, like Bell's HopSlam or Port Brewing's Old Viscosity against the funky creaminess of an oozy, washed-rind monster.
Aromatized wines, like Lillet, vermouth, Americano, or quinquina are great, easy aperitifs, and pair well with most cheeses. Try serving a nice vermouth, like Carpano Antica Formula, or a quinquina like RinQuinQuin over ice, with a citrus twist, and they'll pair passably, at least, with whatever cheese you have on hand. One superlative pairing that immediately springs to mind is a sweet vermouth—try Vya or the aforementioned Carpano Antica—with an herbed cheese, like Brin d'Amour or Tomme de Bordeaux. The strong marjoram notes in the vermouth will play up the delicious, complex herbal bouquet of the cheese.
Madeira, port, and sherry are all fortified wines, but the category encompasses a broad range of flavors and characters, from delicate, dry fino sherry to raisiny, syrupy tawny port. They all share some curry and caramelized notes from the aging and oxidation process, which means that they have an inherent savoriness that helps make them natural pairings for older, richer cheeses like goudas, cheddars, and alpine types. The sweeter side of this family also plays well with blues and washed-rind cheeses.
I have to admit that I only included flavored wines as a separate category for one of my personal favorites: Stone's Original Green Ginger Wine, a syrupy, ginger-infused currant wine which seems, to me, the epitome of Britishness, from its quirky bottle to its strange, medieval taste. It's quite sweet, and as such pairs especially well with tart, acid goat cheeses and mouth-lacerating blue cheeses, but the moderate ginger burn in the background acts as something of a palate-cleanser. Try it either chilled and straight up or, like the aromatized wines, over ice with a lemon twist.
I never get to write about my first love, cocktails, because Paul Clarke already does so much more competently than I could. But let me say that, during cocktail hour at my house, a cheese plate with a couple local cheeses often appears, mysteriously. Since you yourself can control, with some precision, the flavor profile of your 5 o'clock libation, it can be quite easy to come up with a great, synergistic combination. Try a rich, woody Manhattan-style drink with a strong blue or rich alpine, or a citrusy White Lady or Pegu Club variation with a goat cheese. A dry-ish Martini variation can complement some of the richer sheep cheeses, while a tiki drink would go well with... you know, I haven't figured that out, yet. But, please, let me know if you have an idea.