Tiny Invaders
From www.tinywindowsgames.com - A Dynofoo (www.dynofoo.com) Venture
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Tiny Invaders is the smallest Invaders game ever. It runs as a tray icon on your desktop, so you can easily just leave it running all day long :)

Left and right arrows control your fighter, the down arrow fires.

Skull means you lose, smiley face means you win.