Ignore the last link to the JRE provided in Andrew's answer, you need the Sun JDK (5 or 6) instead of just the JRE (The Java Development Kit can contain multiple Java Runtime Environments). The official documentation Android provides makes this distinction quite clear. You need the JDK. --> http://developer.android.com/sdk/installing.html#Preparing
Also, the ADT plugin for eclipse sometimes doesn't update correctly. In that case, try to manually remove the 's' from the 'https://' and if that doesn't work, click on one of the tabs of the dialog and look for the checkbox which forces the use of secure mode, and then of course, make sure there is an 's' in the 'https://'.
Also make sure you've updated your system environment variable called 'path' to make sure the tools inside the tools/ folder from your android sdk folder are accessible from anywhere your command line/Eclipse might decide to call them from.