UPDATE - To combine Andy's method and the Prototyping method...
Array.prototype.sum = function(){
    return this.reduce(function(a,b) {return a+b} );
}
Now all array will have the sum method. eg var total = myArray.sum();.
Original answer...
I'd be tempted with just
var myArray = [1,2,3,4,5];
var sum     = 0;
for (var i=0, iMax=myArray.length; i < iMax; i++){
    sum += myArray[i];
};
alert(sum);
break it out into a function if you're using it a lot. Or even neater, prototype it...
Array.prototype.sum = function(){
    for(var i=0, sum=0, max=this.length; i < max; sum += this[i++]);
    return sum;  
}
var myArray = [1,2,3,4,5];
alert(myArray.sum());
Courtesy of DZone Snippets