1. 유튜브 

function getYouTubeThumbnailImage($video_id) {
    return "http://i3.ytimg.com/vi/$video_id/hqdefault.jpg"; //pass 0,1,2,3 for different sizes like 0.jpg, 1.jpg
}

getYouTubeThumbnailImage('VIDEO_ID');

2. 비메오
function getVimeoThumb($id)
{
	$arr_vimeo = unserialize(file_get_contents("http://vimeo.com/api/v2/video/$id.php"));
	echo $small = $arr_vimeo[0]['thumbnail_small'] ."<br>";
	echo $medium = $arr_vimeo[0]['thumbnail_medium'] ."<br>";
	echo $large = $arr_vimeo[0]['thumbnail_large'] ."<br>";
}

getVimeoThumb('VIDEO_ID');

3. 데일리모션
function getDailymotionThumb($id) {
	$thumbnail_medium_url='https://api.dailymotion.com/video/'.$id.'?fields=thumbnail_medium_url'; //pass thumbnail_large_url, thumbnail_small_url for different sizes
	$json_thumbnail = file_get_contents($thumbnail_medium_url);
	$arr_dailymotion = json_decode($json_thumbnail, TRUE);
	$thumb=$arr_dailymotion['thumbnail_medium_url'];
	echo $thumb;	
}

getDailymotionThumb('VIDEO_ID');