Can You Freeze Cheese?

I freeze hard cheeses like cheddar, buying a large block and cutting it into smaller ones.  The texture is slightly different - more crumbly but I don't find that a problem.  I also grate and freeze parmesan.
I've not tried sliced cheese, but I would think it's fine.  I'd be inclined to remove the cheese from the packaging, separate the slices and interleave them with greaseproof paper or similar.  When you pack into a container include the label from the original packaging for information.

Yes, some may say it affects the taste but it is quite safe. I've done it and the cheese seems to be fine. If you click www.ochef.com here you will find a lot of guidance on which cheeses freeze best and for how long. Also if you look at the bottom of that page there is a link to a page on freezing American sliced cheese.