Well, the most famous sights are the new and old city "Mala Strana" and "Stare Mesto" (in Stare Mesto you'll find the astronomical clock Viggen posted about earlier, with the statues of the apostles coming out of it, it lasts for a minute or so every hour). The Old Town square is fascinating, I can't tell what's so special about it but there's a certain charm about the place, same for Charles Bridge. Not far from there you'll find "Prague's little Venice", they take you around with gondolas and all that lol =)
Another must see is the castle and of course S.Vitus' Cathedral (they will charge you for taking pictures/videos though..). Make sure you take a boat cruise along the Vtlava river, the view of the city from there is lovely, food on the boat is ok as well (strangely enough I didn't miss Italian food lol).
I know you only have 3 days but you should definitely visit Karlovy Vary and Kutna Hora, first one is a thermal city in the middle of Boemia, the landscape is breathtaking, the second is a medieval town (part of the UNESCO world cultural and natural heritage..). I could go on for hours but I'd better stop here
I couldn't resist, webcam here (from behind the Old Town square):
http://dokumenty.prague-city.cz/camera/fullsize.jpg