My absolute favourite cheese is Dubliner cheese, by Kerrygold. It's a lovely Irish cheese that's quite firm, and has a subtle sweetness and nuttiness to it. It's absolutely delightful when shredded over eggs, sliced in a sandwich, melted on nachos, or even just eaten straight.
I'm also rather fond of Cheddar. Give me a good Cheddar, and I'll be happy; the older the better!
Others that I'm fond of include Havarti, Monterey Jack, basically any form of cheese sauce, Mozzarella, Emmental, supermarket Tex Mex cheese blends, Edam, Swiss, and Boursin. Also, add Jalapeno or Habanero flakes to any of them, and I'm pleased.
The best local cheese I've ever tried has to be an aged whiskey cheddar that I found at a local farmer's market in my hometown area. That was absolutely delightful.