Wordpress - How to check if a user exists by a given id

I would highly recommend Daniel's much simpler solution over the one currently selected as correct:

$user = get_userdata( $user_id );
if ( $user === false ) {
    //user id does not exist
} else {
    //user id exists
}

In this case I will definetely not use the get_userdata( $user_id ) while it is returning a WP_User, so it is more greedy than just a custom query.

About the query, I agree using the prepare method, but the SELECT COUNT(*) means you are returning all columns, which is useless here.

I would recommend using SELECT COUNT(ID) unstead, in this way we are only working on a single column which will be faster.

On other aspect for the returning statement, it would be more readable with a Ternary Logic like :

return 1 < $count ? true : false;

To sum up, I wouldd have implemented it like :

function user_id_exists( $user_id ) {
    global $wpdb;
    $count = $wpdb->get_var( $wpdb->prepare( "SELECT COUNT(ID) FROM $wpdb->users WHERE ID = %d", $user_id ) );
    return empty( $count ) || 1 > $count ? false : true;
}

If performance is a concern, use:

function user_id_exists($user_id) {
    global $wpdb;

    // Check cache:
    if (wp_cache_get($user_id, 'users')) return true;

    // Check database:
    if ($wpdb->get_var($wpdb->prepare("SELECT EXISTS (SELECT 1 FROM $wpdb->users WHERE ID = %d)", $user_id))) return true;

    return false;
}

Otherwise, use get_userdata($user_id) !== false. The call to get_userdata will retrieve a whole row from the database instead of a single value, create a new WP_User object and cache it on success.