Starting PHP5.5+ you have array_column() available to you, which makes all of the below obsolete.
$ids = array_map(function ($ar) {return $ar['id'];}, $users);
Solution by @phihag will work flawlessly in PHP starting from PHP 5.3.0, if you need support before that, you will need to copy that wp_list_pluck.
In Wordpress there is a function called wp_list_pluck If you're using Wordpress that solves your problem.
PHP < 5.3If you're not using Wordpress, since the code is open source you can copy paste the code in your project (and rename the function to something you prefer, like array_pick). View source here