There isn't a more certain sign of happiness than a wagging tail, but fortunately this sign is reserved for dogs. How much of a pain in the ass (literally and figuratively) would it be if every time we you were happy, a limb-like appendage at the end of your butt whipped around full speed. Not only would it make walking through narrow doors painful, but it would also make hiding your happiness impossible.
For example, say one of your friends beat you in Mario Kart last weekend, and gloated about it for days. But today he came over to tell you that he lost his video-game thumb in a terrible grapefruit spoon accident. The socially acceptable response is to look aggrieved and say something like, "Holy crap, I always knew those were a dangerous breakfast food." But inside you're overjoyed that he'll never be able to beat you in Mario Kart ever again. And if you had a tail, he'd know just how happy you were to hear about the death of his thumb. You don't want him knowing how cruel you are. Or how seriously you take Mario Kart.
(flickr photo Suppertime by basykes; http://www.flickr.com/photos/basykes/967289880/)