We had a huge beautiful double rainbow (actually, upon further inspection, I think it is a triple rainbow - right underneath the brighter bow the colors repeat, but it doesn't show up really well in the picture.) this evening in Colorado Springs. I took a few pictures that don't do it justice and posted them here.
"And God said, This is the token of the covenant which I make between me and you and every living creature that is with you, for perpetual generations: I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth. And it shall come to pass, when I bring a cloud over the earth, that the bow shall be seen in the cloud: And I will remember my covenant, which is between me and you and every living creature of all flesh; and the waters shall no more become a flood to destroy all flesh. And the bow shall be in the cloud; and I will look upon it, that I may remember the everlasting covenant between God and every living creature of all flesh that is upon the earth. And God said unto Noah, This is the token of the covenant, which I have established between me and all flesh that is upon the earth."
As far as I can tell, the rainbow is nowhere mentioned in the Qur'an.
I did find this hadith from Imam Hasan (as):
"Regarding the rainbow, you should not name it 'Quzah ---the bow of Quzah-' because 'Quzah' is the name of a devil.
You should name it 'Qawsullah---the bow of Allah-'. It is security against drowning."
Now, this could refer to the mercy covenant mentioned in the Bible, or it could also refer to the simple science of rainbows - in order for the rainbow to appear, the sun must be shining into the rain, which means that clearer skies are around the area of the rain and thus there will not be enough to threaten flooding.
Please let me know if you find any other religious references to rainbows, I'd love if people would share them.
In any case, rainbows are beautiful signs and are merciful if for no other reason than their beauty and the rain associated with them.