Mild beers with mild cheeses. For example a mozzerella or something of that sort would go well with a pilsner or farmhouse ale.
For washed rind cheeses like tellegio, strong fruity belgians.
Aged hard cheeses like cheddar go well with bold beers something with a punch to combine with the punch of the cheese, like an IPA, Stout, or porter.
For blues it's go big or go home. Anything with the imperial title usually is good (though I'd go with an IIPA over an Imperial stout) and barley wines.