Open up Disk Management (right click on My Computer, click on Manage) and see in the bottom graphical section if your external drive is recognized, if it has a dark blue band above, has a drive letter assigned to it, and says health drive. Report back any other or different findings.
Also you might conect it to a different computer, and see if it is recognized there.
What OS are you using?
Always click on the "safely remove this device" icon in the system tray before removing the connector to an external HDD, or better yet, shut the computer off before removing or attaching an external USB or eSATA HDD.