Can I use cottage cheese instead of cream cheese when making a cheesecake? If I can, would there be any difference in the measurements? For example if the recipe calls for 8 ounces of cream cheese, would it be the same amount of cottage?
I've made cheesecake with many different types of cheese and it pretty much always worked. 

Of course texture and taste vary, but that's the beauty of it. Try a single cheese, see what it gives and then start experimenting mixing them.

For instance cottage cheese tends to give a slightly more "crumbly" texture. To compact it you can add some fresh cream. 

Sour cream also makes a wonderful addition, and marries well with some lemon zest, taken that you like a bit of acidity in your cake.

I've also tried to add mascarpone and even gorgonzola, they all work well, and give you very peculiar mouth-feelings to combine and mix as you please, but obviously add in calory content quite a bit...

As for the amount, you an just keep the same as cream cheese.