Good point, the brewing method totally affects the brew you get out. You should never leave the coffee in too long otherwise all kinds of bitter flavors come out into the brew, which is why percolator coffee is almost as bad as cowboy coffee. A proper drip machine would limit the water-coffee contact time. Also, the correct temperature is close to 200F, not easy to do in a teacup.

For espresso (my favorite method) the best quality is had when the extraction time is 20-25 seconds. Any more, and the coffee gets thin and bitter. In Illy's book on coffee, there's a nice picture where they swapped out the cups every few seconds while making an espresso, the first few cups have a nice red-brown color, the later ones are yellow and pale.