I have found a very effective way to remove "red eyes" in Photoshop.

Before

After
1. Choose a brush, which is just a little bit wider than the middle (dark/red) part of the eye. It is probably best to "zoom in" the eye to get a more exact brush size. Make sure to set the hardness of the brush to 0 (that is, no sharp edges).
2. Double-click the sponge tool and choose decrease the saturation and set the pressure to 100%.
3. Click a couple of times in the middle (dark/red) part of the eye and that’s it.
There are a number of ways to reduce the red eye effect, for example to paint with black on top of the red part, but then you loose the light reflex, which is natural in a human eye.
I use the Swedish version of Photoshop, so the names of the tools are different in Swedish, but if you look at the screendump below, you might find it easier to see what I mean.

