In general the colors would take on a yellowish hue. The colors that are most damaged by sunlight are white and blue. White can turn all the way to dark tan, and blue will take on an ugly yellowish color. On the other hand red would fade into pink. But again; the sun does damage the bricks. They will turn brittle and somewhat powdery, like all plastics do.
If you want to change the color of LEGO bricks I recommend vinyl-dye that fuses with the plastic so there is no build-up and it won't scratch off easily. There is a limited color choice, but this is an excellent way to change the color if you really have to. My favorite brand is Plasti-kote Vinyl Color available at auto-supply stores. Quite expensive though and hard to find. Another brand is Krylon Fusion for Plastic, readily available at Wal-Mart and other places. The fusing is not nearly as good as with Plasti-kote, but it is still quite durable. The price is better and there are more color choices.
Another method would be using RIT dye (use the powdered form not the liquid), but I don't like this method as much because although the colors can turn out nice (they are pastel colors - kind of like what you find in LEGO Friends sets), but they do fade with age.
If you want to try the sun-method, just place outside some cheap elements and you will see what happens. Please note that the colors will continue to turn darker (in the case of white) even after you removed them from the sun. Kind of like how a sunburn continues to get worse even after you go in the shade...(c;
