I was also met with this speech popup a few weeks ago. It can be turned on or off system-wide, but is sometimes app-specific for when it appears. For me, it was because I was using the Chess app, which uses "Speakable Items" so that the player can speak moves.

I had to uncheck "Allow Player to Speak Moves" in the Chess preferences pane. Depending on the application, you may or may not be able to disable this option.

You can disable "Speakable Items" system-wide through System Preferences by opening the Accessibility pane and scrolling down to "Speakable Items" and ticking the Off radio button.

I was also met with this speech popup a few weeks ago. It can be turned on or off system-wide, but is sometimes app-specific for when it appears. For me, it was because I was using the Chess app, which uses "Speakable Items" so that the player can speak moves.

I had to uncheck "Allow Player to Speak Moves" in the Chess preferences pane. Depending on the application, you may or may not be able to disable this option.

You can disable "Speakable Items" system-wide through System Preferences by opening the Accessibility pane and scrolling down to "Speakable Items" and ticking the Off radio button.

Sources:

eHow Source for disabling Speakable Items

Apple Discussion