They shouldn't, but they do tend to have a large quantity of memory backing them that gets added to when grown into. The kernel uses 4k, 8k, or 16k stacks; a quick test on a Linux x86-64 system suggests that userspace has 8M stacks by default.

Hackish test code to recurse infinitely and print the stack pointer until a segfault:

    #include <stdio.h>

    static inline unsigned long get_sp(void)
    {
        unsigned long ret;
        __asm__("mov %%rsp, %0" : "=r" (ret));
        return ret;
    }

    void main(void)
    {
        printf("%lu\n", get_sp());
        main();
    }

Running this and comparing the first and last values shows a stack size of about 8M.