Of course it is perfectly correct in terms of grammar to speak without contractions. Here in the southern United States, however, we use contractions all the time, even in formal situations, and it would it come across as a little mechanical not to use them.
Edit: Su.Ki. is right, this isn't really a regional issue. I just mention the US South because here we even use contractions that are not grammatically correct, such as "ain't" and "y'all."