Google sent out an email to all Google video users saying that the service will no longer be available come May 13th. They said that users who have videos up on Google video will be able to download their videos via a download button that Google will add to the page. On April 29th, videos that are on Google video will not longer be available for playback and users have till May 13th to download their videos. If you don't want to download your video, you, of course, don't have to do anything.
Google recommends users upload their videos to YouTube after downloading. For users who have multiple videos up on Google video, they recommend using the paging controls on the bottom right of the screen. To download your video, go to the video status page, and then click on download video on the right side of the video in the action column.
This shut down has been a long time coming, especially since Google bought YouTube in 2006. They stopped uploads to Google video in May 2009 in their attempt to make YouTube profitable. Shutting down Google video just seemed like the obvious next step.