Hmm, what have I currently got lurking in the fridge...
Brie, Brie with truffle (damn bloody gorgeous), Caprices des Dieux, Tesco extra mature Cheddar*, Davidstow 18 month matured Cheddar, a vintage Red Leicester, that whacking great big lump of Gruyere, Grana Padano (Parmesan by any other name - it's the same cheese, but made out of the protected region), Provolone Piccante and some squishy Italian thing that I think is called Burrata.
* I use this for cooking and sandwiches, but it's actually a very nice cheddar in its own right. You wouldn't be embarrassed putting it on a cheese board, as it would please most people.
Rind... If the cheese squishes, I'll eat it, if it doesn't, I don't.