Stride is used in at least two operations: convolution and pooling. Both operations can be viewed as applying a kernel function on input using a kernel (filter).
Stride determines the amount of "jump" the kernel needs to perform on the input. Obviously, in the extreme case, if the kernel size and stride is one, the input size is the same as the output size. In all other cases, the output size is less than the input size.
So, I am guessing that down-sampling is the only purpose of using stride in any case. Am I true? Else, are there any cases in which stride is used in order to serve another purpose?