I know it's the cheese equivalent of vanilla ice cream but I like strong cheddars, either crumbly like Balderson (peaks around 3 Years, the 5 Years is too dry for my tastes) or smooth like Agropur (where I prefer the 1 Year over the higher vintages).
Also Emmental (the cheese most people mean when they say "Swiss Cheese"; there's also Gruyère but I find Gruyère too dense).