Many countries of origin prohibit dual citizenship and force their citizens to choose between either the old or the new citizenship. Other countries such as Germany and Austria allow it under certain conditions which you must demonstrate concretely in an application to your country of origin. It is generally important to have all special permits to hand before accepting Canadian citizenship. For Germany and Austria, we can recommend you a very experienced law firm for these matters.
Other countries such as Switzerland are very generous in allowing multiple citizenship.