What causes cats/dogs/animals eyes to shine an eery red at night when a flashlight is pointed at them?
Not always red – my shepherd/lab mix’s eyes shine bright Kryptonite green! Our springer puppy’s eyes used to shine that color too, but now that she’s older they’re just plain red.
I asked my vet once about the color difference, and he had no idea.
The tapetum lucidum.
Both my dogs glow green as well. I always wanted to take a slow-exposure photograph of it, but even the Grumpy Old Lady Dog would never stand still for that long.
I suppose you include people in the “animals” definition. In low light levels the pupil dilates and allows you to see the back of the eye, the retina. The lens of the eye concentrates the effect. This is what causes red eye in flash photos.
First a quick quote from that site zgystardst posted…
Here is a question.
So it is because of this reflecting membrane that animals have great night vision? So what is to keep us from making a slightly reflective contact lens that has the same effect? Could better night vision be had this way?
Although the reflectivity of the lens would decrease re-transmission of the light to the outside of the eye, the necessary decreased transmissivity inherent in a partially reflective surface would attenuate the amount of light entering the eye in the first place. Think mirrored sunglasses.
Because the flashlight is more effective! 
I remember this question addressed in the Straight Dope Mailbag.