Too much is probably bad for them... eggs are awfully rich. But we used to feed our cats an egg (scrambled, not hard boiled) for a treat, and it never bothered them.
I know for a fact that eating too many hard boiled eggs will give a dog terrible gas...
One year for Easter, Dad had the brilliant idea to hide the (real, dyed) Easter Eggs around the house before bed so we could hunt for eggs when we woke up. (There was about 2 feet of snow on the ground that year.) He heard and *crunch crunch* noise a few times that night, but didn't really think much of it. Well, our Weimeriener Dutchess had gone hunting eggs in the middle of the night and found ALL of them - a whole dozen, I think. She had a very upset stomach, horrible gas, and I'm sure she had diarreah too. Poor thing... She was an outside dog for that Easter Sunday!
I read that whites by themselves deplete some vitamin in dogs, but a whole egg is fine as the yolk replaces whatever it was. I think one a week is fine.
Sure its fine - just chop it up good and let them enjoy. An occasional egg or two won't hurt. We usually save part of scrambled eggs for the dog and cats as a treat.