How do I get a YouTube video thumbnail from the YouTube API?

You can use YouTube Data API to retrieve video thumbnails, caption, description, rating, statistics and more. API version 3 requires a key*. Obtain the key and create a videos: list request:

https://www.googleapis.com/youtube/v3/videos?key=YOUR_API_KEY&part=snippet&id=VIDEO_ID

Example PHP Code

$data = file_get_contents("https://www.googleapis.com/youtube/v3/videos?key=YOUR_API_KEY&part=snippet&id=T0Jqdjbed40");
$json = json_decode($data);
var_dump($json->items[0]->snippet->thumbnails);

Output

object(stdClass)#5 (5) {
  ["default"]=>
  object(stdClass)#6 (3) {
    ["url"]=>
    string(46) "https://i.ytimg.com/vi/T0Jqdjbed40/default.jpg"
    ["width"]=>
    int(120)
    ["height"]=>
    int(90)
  }
  ["medium"]=>
  object(stdClass)#7 (3) {
    ["url"]=>
    string(48) "https://i.ytimg.com/vi/T0Jqdjbed40/mqdefault.jpg"
    ["width"]=>
    int(320)
    ["height"]=>
    int(180)
  }
  ["high"]=>
  object(stdClass)#8 (3) {
    ["url"]=>
    string(48) "https://i.ytimg.com/vi/T0Jqdjbed40/hqdefault.jpg"
    ["width"]=>
    int(480)
    ["height"]=>
    int(360)
  }
  ["standard"]=>
  object(stdClass)#9 (3) {
    ["url"]=>
    string(48) "https://i.ytimg.com/vi/T0Jqdjbed40/sddefault.jpg"
    ["width"]=>
    int(640)
    ["height"]=>
    int(480)
  }
  ["maxres"]=>
  object(stdClass)#10 (3) {
    ["url"]=>
    string(52) "https://i.ytimg.com/vi/T0Jqdjbed40/maxresdefault.jpg"
    ["width"]=>
    int(1280)
    ["height"]=>
    int(720)
  }
}

* Not only that you need a key, you might be asked for billing information depending on the number of API requests you plan to make. However, few million requests per day are free.

Source article.

What Asaph said is right. However, not every YouTube video contains all nine thumbnails. Also, the thumbnails' image sizes depends on the video (the numbers below are based on one). There are some thumbnails guaranteed to exist:

Width | Height | URL
------|--------|----
120   | 90     | https://i.ytimg.com/vi/<VIDEO ID>/1.jpg
120   | 90     | https://i.ytimg.com/vi/<VIDEO ID>/2.jpg
120   | 90     | https://i.ytimg.com/vi/<VIDEO ID>/3.jpg
120   | 90     | https://i.ytimg.com/vi/<VIDEO ID>/default.jpg
320   | 180    | https://i.ytimg.com/vi/<VIDEO ID>/mq1.jpg
320   | 180    | https://i.ytimg.com/vi/<VIDEO ID>/mq2.jpg
320   | 180    | https://i.ytimg.com/vi/<VIDEO ID>/mq3.jpg
320   | 180    | https://i.ytimg.com/vi/<VIDEO ID>/mqdefault.jpg
480   | 360    | https://i.ytimg.com/vi/<VIDEO ID>/0.jpg
480   | 360    | https://i.ytimg.com/vi/<VIDEO ID>/hq1.jpg
480   | 360    | https://i.ytimg.com/vi/<VIDEO ID>/hq2.jpg
480   | 360    | https://i.ytimg.com/vi/<VIDEO ID>/hq3.jpg
480   | 360    | https://i.ytimg.com/vi/<VIDEO ID>/hqdefault.jpg

Additionally, the some other thumbnails may or may not exist. Their presence is probably based on whether the video is high-quality.

Width | Height | URL
------|--------|----
640   | 480    | https://i.ytimg.com/vi/<VIDEO ID>/sd1.jpg
640   | 480    | https://i.ytimg.com/vi/<VIDEO ID>/sd2.jpg
640   | 480    | https://i.ytimg.com/vi/<VIDEO ID>/sd3.jpg
640   | 480    | https://i.ytimg.com/vi/<VIDEO ID>/sddefault.jpg
1280  | 720    | https://i.ytimg.com/vi/<VIDEO ID>/hq720.jpg
1920  | 1080   | https://i.ytimg.com/vi/<VIDEO ID>/maxresdefault.jpg

You can find JavaScript and PHP scripts to retrieve thumbnails and other YouTube information in:

• How to get YouTube Video Info with PHP
• Retrieve YouTube Video Details using JavaScript - JSON & API v2

You can also use the YouTube Video Information Generator tool to get all the information about a YouTube video by submitting a URL or video id.

In YouTube API V3 we can also use these URLs for obtaining thumbnails... They are classified based on their quality.

https://i1.ytimg.com/vi/<insert-youtube-video-id-here>/default.jpg -   default
https://i1.ytimg.com/vi/<insert-youtube-video-id-here>/mqdefault.jpg - medium 
https://i1.ytimg.com/vi/<insert-youtube-video-id-here>/hqdefault.jpg - high
https://i1.ytimg.com/vi/<insert-youtube-video-id-here>/sddefault.jpg - standard

And for the maximum resolution..

https://i1.ytimg.com/vi/<insert-youtube-video-id-here>/maxresdefault.jpg

One advantage of these URLs over the URLs in the first answer is that these URLs don't get blocked by firewalls.

If you want the biggest image from YouTube for a specific video ID, then the URL should be something like this:

http://i3.ytimg.com/vi/SomeVideoIDHere/0.jpg

Using the API, you can pick up default thumbnail image. Simple code should be something like this:

//Grab the default thumbnail image
$attrs = $media->group->thumbnail[1]->attributes();
$thumbnail = $attrs['url'];
$thumbnail = substr($thumbnail, 0, -5);
$thumb1 = $thumbnail."default.jpg";

// Grab the third thumbnail image
$thumb2 = $thumbnail."2.jpg";

// Grab the fourth thumbnail image.
$thumb3 = $thumbnail."3.jpg";

// Using simple cURL to save it your server.
// You can extend the cURL below if you want it as fancy, just like
// the rest of the folks here.

$ch = curl_init ("$thumb1");
curl_setopt($ch, CURLOPT_HEADER, 0);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_BINARYTRANSFER,1);
$rawdata = curl_exec($ch);
curl_close($ch);

// Using fwrite to save the above
$fp = fopen("SomeLocationInReferenceToYourScript/AnyNameYouWant.jpg", 'w');

// Write the file
fwrite($fp, $rawdata);

// And then close it.
fclose($fp);

If you want to get rid of the "black bars" and do it like YouTube does it, you can use:

https://i.ytimg.com/vi_webp/<video id>/mqdefault.webp

And if you can't use the .webp file extension you can do it like this:

https://i.ytimg.com/vi/<video id>/mqdefault.jpg

Also, if you need the unscaled version, use maxresdefault instead of mqdefault.

Note: I'm not sure about the aspect ratio if you're planning to use maxresdefault.