remove dictation icon from desktop

You are referring to Speakable Items. To turn it off, open System Preferences > Accesibility > Speakable Items, and turn off Speakable Items, so the Speakable Items icon will disappear from Desktop

You are welcome

As mendes1 rightly indicated, disabling Speakable Items in the System Preferences will make the icon disappear from the Desktop... most of the time.

However there is a case mentioned in another discussion where the icon won't get away by itself. Is is when the Chess game is running, whether active or in the background. You then have to quit it, forcibly if necessary, before the icon would disappear.

We might deduce from that also that if the icon won't go away even when Speakable Items is disabled, then one has to quit all applications one by one to see which kept it on the desktop.

These comments apply for OSX 10.7 Lion.