Each YouTube video has 4 generated images. They are predictably formatted as follows:

http://img.youtube.com/vi/<insert-youtube-video-id-here>/0.jpg
http://img.youtube.com/vi/<insert-youtube-video-id-here>/1.jpg
http://img.youtube.com/vi/<insert-youtube-video-id-here>/2.jpg
http://img.youtube.com/vi/<insert-youtube-video-id-here>/3.jpg

The first one in the list is a full size image and others are thumbnail images. The default thumbnail image (ie. one of 1.jpg, 2.jpg, 3.jpg) is:

http://img.youtube.com/vi/<insert-youtube-video-id-here>/default.jpg

For the high quality version of the thumbnail use a url similar to this:

http://img.youtube.com/vi/<insert-youtube-video-id-here>/hqdefault.jpg

There is also a medium quality version of the thumbnail, using a url similar to the HQ:

http://img.youtube.com/vi/<insert-youtube-video-id-here>/mqdefault.jpg

For the standard definition version of the thumbnail, use a url similar to this:

http://img.youtube.com/vi/<insert-youtube-video-id-here>/sddefault.jpg

For the maximum resolution version of the thumbnail use a url similar to this:

http://img.youtube.com/vi/<insert-youtube-video-id-here>/maxresdefault.jpg

All of the above urls are available over https too. Just change http to https in any of the above urls. Additionally, the slightly shorter hostname i3.ytimg.com works in place of img.youtube.com in the example urls above.

Alternatively, you can use the YouTube Data API (v3) or the older YouTube API v2.0 to get thumbnail images.