PHP

<?php

function f(&$r, $t, $a, $n)
{
    if ($n == 0) {
        if (count($t)) {
            $r[] = $t;
        }
    } else {
        $count = count($a[$n - 1]);
        for ($i = 0; $i < $count; $i++) {
            f($r, array_merge($t, [$a[$n-1][$i]]), $a, $n - 1);
        }
    }
}

function combine($arr)
{
    $r = [];
    f($r, [], $arr, count($arr));
    return $r;
}

$arr = [
    [1, 2],
    [3, 4],
];
print_r(combine($arr));

// preview
Array
(
    [0] => Array
        (
            [0] => 3
            [1] => 1
        )

    [1] => Array
        (
            [0] => 3
            [1] => 2
        )

    [2] => Array
        (
            [0] => 4
            [1] => 1
        )

    [3] => Array
        (
            [0] => 4
            [1] => 2
        )

)

Javascript

function combine(arr) {
    var r = [];
    (function f(t, a, n) {
        if (n == 0) return t.length ? r.push(t) : r;
        for (var i = 0; i < a[n-1].length; i++) {
            f(t.concat(a[n-1][i]), a, n - 1);
        }
    })([], arr, arr.length);
    return r;
}
var arr = [
    ['1', '2'],
    ['3', '4']
];
var res = combine(arr);
console.log(res);
// preview
[["3","1"],["3","2"],["4","1"],["4","2"]]