Handicap placement
Here are the traditional placements for handicap stones under Japanese Rules. Other rules, such as Chinese rules, allow free handicap placement.
Andrew Grant: It is a fallacy that Japanese rules do not allow free handicap placement. In fact the official Japanese rules say nothing at all about handicap placement. It's true that the fixed pattern is universally used in Japan, but this is just a tradition, nothing more.
One handicap stone
The weaker player plays Black without komi.
Two handicap stones
Joshual000: I believe upper left is left open for 'polite-ness' shown by Black to White (Black's 1st move is the one held by tradition - not White's)
Four handicap stones
JoB: i think this is the european version. as far as i know the japanese put the 5th (and 7th) stone on one of the 10-4 points,
kokiri - this is how the japanese play 5 stones,