A cheese board is a complete minefield where wine is concerned but White wines generally fare better than Reds. There is no real sure fire winner here but a rich full-bodied Chardonnay will go with more types of cheeses than most wines. It is actually much better to serve just one or two great cheeses with a well-matched wine than a big cheese selection.
Sauternes or Barsac
These are two of the food and wine matches made in heaven. Gorgonzola:
Gorgonzola is not easy to match but a Bual Madeira or an aged Tawny Port would be OK.
Mild creamy cheeses like Cambozola work quite well with a Tokaji Aszú or other sweet wines.
Dolcelatte being that bit stronger would work with aged Spanish Red from Rioja, Navarra or Ribera del Duero and Amarone from Veneto.
Goats' Cheese has a real affinity with Sauvignon Blanc. Sancerre or Pouilly Fumé are perfect or a New Zealand Sauvignon nearly as good.
Cheddar, Red Leicester, Gruyere, Parmesan and Manchego:
Medium to Full-Bodied Dry Reds
Hard cheeses probably fare better with Red wines than any other type of cheese. For Cheddar, Red Leicester, Gruyere, Parmesan and Manchego, medium to full-bodied dry Reds like mature Red Bordeaux or even a mature Rioja work as would a rich, full-bodied Chardonnay such as White Burgundy.
Smoked Cheese is very difficult to match, try an Alsace Gewurztraminer.
Camembert or Chaumes:
Mouth-coating soft cheeses are very problematical with Red wines. However both Camembert and Chaumes work fine with a Red Burgundy or a ripe Pomerol or St. Emilion wines.
For Brie choose a rich White Burgundy and a steely Chablis for Chaource.