Kids tend to love American cheese and many really do not want anything to do with any other type of cheese. The problem with this is that the American sliced cheese is a processed cheese product. It is not as healthy or as easy to digest as other types of cheeses are. The best thing you can do for your children, no matter how old they are, is to expose them to a wide variety of different foods, which will include different cheeses.
Of course, if you can get your kids to try different cheese options on their own, this would be ideal. One of the best ways to go about this would be to go out, purchase a large variety of cheeses and then make a cheese and cracker platter at home. Get the kids involved in the creation of the cheese and cracker platter. If they are old enough, have them help cut the cheese or simply have them arrange everything on the platter.
Praise them for all of their hard work and make sure that you are super impressed at the taste of all of the cheese that they placed on the platter. Before you know it, your kids will be trying all of the different cheese options as well.
If none of this works, you could always sneak the different kinds of cheese into their favorite foods. They will be able to tell that cheese was added but what kid is going to fight cheese being added to their meal? After they finish everything, you will want to make sure that you casually mention what cheese was used.
Before you know it, you will find that your kids are well versed on the different kinds of cheese and that they are more than willing to try new types and flavors as you come across them.