Yes, in most cases you are encouraged to eat the rind.
If the cheese is wrapped in a fabric-like bandage or wax, you should not eat the rind. Swedish Fontina is a great example of a cheese that you would first need to take off the wax rind before eating.
There are some implications with regard to etiquette. In 99% of cases where you are being served cheese, if you were only to eat the paste (the interior of the cheese) it would be like eating chicken wings and then putting the bones back on the plate they were served on. It's not pretty and is inconsiderate for others that might like to try some. Brie is notorious for having very specific etiquette, and consuming both the rind and the paste together is one of them.
Some older aged cheeses can have some pretty funky, chewy rinds–that seem wholly unappetizing. In those cases, you'll have to think about what works best for you. If you're preparing the cheese yourself, to be perfectly honest, you may just be doing it wrong. You may want to head over to your nearest restaurant that serves cheese and have a professional show you how it's done before you make up your mind about a funky rind.
At the end of the day, you eat different foods because they taste good to you; so, if you don't like any part of the cheese, don't eat it.