getNumLinks() //gets the number of linked objects attached to object

//Special thanks to Lance LeFay, Bosozoku Kato, and Ironchef Cook who helped me out with debugging this function

integer getNumLinks() //returns the number of objects linked to object calling function.
{
    if(llGetLinkKey(0) != NULL_KEY) return -1; //Object is alone

    else
    {
        integer i = 1; //skip 0, since 0 is already checked
        while(TRUE)
        {
            if(llGetLinkKey(i) == NULL_KEY)
            {
                return i - 2; //the object script is on, and the number that returned NULL_KEY
            }
            else 
            {
                i++;
            }
        }
    }
}

A simple variation on the function above can return the total number of objects in the linked set, instead of the objects linked to the function caller object, simply change return i - 2; to return i - 1;

-Chris

Some "improvements"

integer getNumLinks() //returns the number of objects
                                //linked to object calling function.
{
    if(llGetLinkKey(0) != NULL_KEY) return -1; //Object is alone

    else
    {
        integer i = 3; //skip 0, since 0 is already checked.
                            //since you checked 0, you already know
                            //that 1 & 2 exist, too.  (1=root, 2=first child)
        while(TRUE)
        {
            if(llGetLinkKey(i++) == NULL_KEY)
            {
                return i - 3; //the object script is on, 
                                 //and the number that returned
                                 //NULL_KEY, and the extra increment
            }
        }
    }
}