Finding matches between multiple JavaScript Arrays

Assuming there is an array of arrays those we want to find the intersection of, a simplest single liner approach could be

var arr = [[0,1,2,3,4,5,6,7,8,9],[0,2,4,6,8],[4,5,6,7]],
    int = arr.reduce((p,c) => p.filter(e => c.includes(e)));

document.write("<pre>" + JSON.stringify(int) + "</pre>");

var result = arrays.shift().filter(function(v) {
    return arrays.every(function(a) {
        return a.indexOf(v) !== -1;
    });
});

DEMO: http://jsfiddle.net/nWjcp/2/

You could first sort the outer Array to get the shortest Array at the beginning...

arrays.sort(function(a, b) {
    return a.length - b.length;
});

For completeness, here's a solution that deals with duplicates in the Arrays. It uses .reduce() instead of .filter()...

var result = arrays.shift().reduce(function(res, v) {
    if (res.indexOf(v) === -1 && arrays.every(function(a) {
        return a.indexOf(v) !== -1;
    })) res.push(v);
    return res;
}, []);

DEMO: http://jsfiddle.net/nWjcp/4/