Yes, for example, if a function is just to print out "hello world", or some calculation, then it can take no parameter, and doesn't need to return any value at all.
For example, you can have a PHP function
function printPageFooter() {
echo "<p>Thanks for coming. Come back soon!</p>\n";
}
that actually prints out the webpage's footer in HTML. This function takes no parameter and print something out, and doesn't return anything.
If it is a language such as C, then when you say
void PrintPageFooter() {
/* do something */
}
you are saying this function doesn't return anything by using the "void" in front of the function definition.
I remember in Pascal, when I learned it long time ago, all functions have to return something. If it doesn't, then it is a "procedure" instead.