secretSanta.js

function secretSanta(array) {
    var year = (new Date).getYear(),
		offset = year % array.length,
		map = {};

	array.forEach(function (item, index) {
		map[item] = array[index + offset] || array[array.length - (index + offset)];
	});

	return map;
}

secretSantaOnce.js

function secretSanta(array) {
    var map = {},
        giveTo = array.slice(0);
    
    giveTo.unshift(giveTo.pop());
    
    array.forEach(function (item, index) {
        map[item] = giveTo[index];
    });
    
    return map;
}