Live demo: https://eval.in/88626
Try this:
create a new array with id as key like this:  
 $countries = array(
    array('ID' => '8','Country' => 'Finland','Currency' => 'EUR'),
    array('ID' => '9','Country' => 'France','Currency' => 'EUR')
);
$outArray = array();
foreach($countries as $country){
 $outArray[$country['ID']] = $country;
}
access your array by its id like this
print_r($outArray[8]['Country']);
Output:
 Finland
Update for search:
Live demo : https://eval.in/88651 
$countries = array(
        array('ID' => '8','Country' => 'Finland','Currency' => 'EUR'),
        array('ID' => '9','Country' => 'France','Currency' => 'EUR')
    );
$r1 = getArrayById($countries,8);
$r2 = getArrayById($countries,'Finland');
$r3 = getArrayById($countries,'EUR');
  print_r($r1);
  print_r($r2);
  print_r($r3);
function  getArrayById($countries,$val){
 $outArray = array();
  foreach($countries as $country){
     if(in_array($val,$country)){
       $outArray[$country['ID']] = $country;
      }
    }
    return $outArray;
}
Output:
Array
(
    [8] => Array
        (
            [ID] => 8
            [Country] => Finland
            [Currency] => EUR
        )
)
Array
(
    [8] => Array
        (
            [ID] => 8
            [Country] => Finland
            [Currency] => EUR
        )
)
Array
(
    [8] => Array
        (
            [ID] => 8
            [Country] => Finland
            [Currency] => EUR
        )
    [9] => Array
        (
            [ID] => 9
            [Country] => France
            [Currency] => EUR
        )
)