There are no hard rules, but match the weight of the red to the cheese. Here is how it works on my wine pairing chart:

• A light red like Pinot Noir: softer cheeses, such as Camembert, feta and goat cheese.
• Merlot: the most flexible of the reds. It goes with the widest range of cheeses, including aged Gouda, cheddar, Camembert, Parmesan, blue, Gruyère, Brie and Manchego.
• Fuller reds like Cabernet Sauvignon: aged Gouda, cheddar and Parmesan. The fat in an aged cheese helps balance the tannins.
• Chianti: provolone and mozzarella.

Be careful with very tannic reds and very salty cheeses: salt tends to make tannins feel harsher. Blue cheese is usually better with a sweet wine like port.

Related: Pairing cheese: wine · What wine or whiskey goes with cheese? · What are tannins in wine?