Not the dictation function per se, but Mac OS X has had this function since the beginning (actually, since before OS X). They've moved it in Mountain Lion (possibly before), but it still exists.
Open System Preferences, and click on Accessibility. Click Speakable Items on the left, and set a listening key (note that you cannot use the same shortcut as dictation, but you could potentially just hold down the function key instead of double tapping or a similar command if you chose). Then, you can say "Open Safari" or any other application you want and it will launch it. You can also click on the Commands tab in that window to see the other things you can say. It's not nearly as advanced as Siri, and less accurate, but it does work well enough once you train it.