Commodore 64 BASIC - 313 chars
EDIT: See below for the golfed version
A little trip down the memory lane with PET graphics, POKEs and PEEKs and everything :)
The program operates directly in the screen memory, so you just go ahead, clear the screen, place your dots, and type RUN:
You have to wait a minute or so while it finds the dots and then it starts to draw. It isn't fast - you can actually see the lines being drawn, but that's the coolest part :)
Golfed version:
Commodore BASIC seems like a great language for golfing, because it doesn't require whitespace :) You can also shorten most of the commands by entering an unshifted first letter followed by a shifted second letter. For example, POKE can be typed as P[SHIFT+O], which appears as P┌ on the screen:
