Playing a non-human race purely for the appearance actually has a use that cannot ever be fulfilled by a human of any kind: a different physiological perspective. You play a race with good senses so you can think about having a wider view of the world, you play a race stronger than a human so you can imagine their ability to move objects with ease.
Cat's got a good point. And I'm actually gonna try and be serious for a moment here.
If someone has already mentioned some of these ideas then excuse me. I've been pressed for time lately and haven't had much time to read other than late at night.
I don't care much for a freak race with a set of built in goat horns. Not as a physiological concept. Not as a mythological character type.
However there is a definite and historical sort of mythological type that these freak races actually embody: Chimeras.
What they are is actually a sort of (badly imagined in my opinion) reinterpretation of the Centaur, and of various other classical myths in which a man possess a trait, or perhaps multiple traits, of other creatures and beings (usually animals or gods).
Now the day is coming, when it will be possible (legally perhaps not, but illegally certainly) when the genetic code of men can be reinterpreted to some degree by the addition of or replacement of non-human genetic material(s). Imagine if you will a man with eyes that had the ability to have multiple focal points, or with eyes that could operate in the same basic way as that of an eagle. Given human physiological limitations to the olfactory cavities imagine men with a near equivalent sense of smell to that of a bloodhound, or maybe even a grizzly bear.
How would that change not only a man's physiological capabilities, but his psychological outlook as well? Suppose a man possessed the nose of a grizzly bear (not in appearance, but in capability). How would this effect his psychological outlook if he could "smell death or corpses" from miles away? How sensitive would he be to pheromones? What if he could see into the ultraviolet range of the electromagnetic spectrum? Or what if hi eyes possessed natural night-vision? How would this effect not just his senses, but his mind? Maybe even his soul?
I think the Greeks, in their many exploration of the Chimera-myth were actually trying to imagine different psychological effects of, "what would a man be like if he possessed some of the peculiar and amazing and very advanced (by human standards) capabilities of the animals surrounding him?" An eagle eye is not worth his brain, being able to hear like a dog is not worth his mind, but would it not give his mind a different cast in interpreting the world? It would give me a different frame of reference, that is for sure. Eagle eyesight, infra-red vision, nightvision, dog-hearing, being able to smell like a bear, would give an incredible range and array of "new intelligence" sources that are now lacking in human beings.
Now that being the case I'll give an example of how this might play out in-game. A few months back I played a Dragonborn Ranger. I didn't like the idea of playing a freak race and didn't think I'd have any interest or sympathy with the character. But I do very much like Rangers, and I was assigned the character. Well, after a few missions and a couple of fights I suddenly realized that what I really had in my Dragonborn Ranger was nothing less than "a real Chimera." An animal sharing certain basic traits with a man and in basically an upright, man-shape.
So at that point I tried to imagine the character very much like trying to imagine myself playing one of my Great Danes. (And over the years I have conducted several experiments with developing "parallel intelligence" in animals.) I tried to imagine the "actual physiological capabilities" of the Dragonborn, and of how to best exploit those capabilities in-game, and then tried to imagine what would be the corresponding psychological effects upon such a character? What I discovered was not only that the Dragonborn was an amazingly efficient and effective character, but he was a lot of fun to play, not as a man, or as a Lizard-slash-Dragon man, but as a Chimera. A mix between man and beast. (This is another point at which I don't think the designers do such a good job, they just basically created "human outcast cultures," with many of the new races, and to a large extent I think human-Chimeras, or Chumeras -humans with animal capabilities - would indeed develop a sort of outcast sub-culture, but then again I think they would also have very, very different ways of looking at the world at large, not just their various cultural interactions. (For one thing if you had the mind of a man and the sensory capabilities of an animal I think this would profoundly reshape religious expression, perceptions, and spiritual outlook and methods.) Physiologically, psychologically, mentally, maybe even spiritually. I can't say that for sure, I am not a chimera, but I strongly suspect my Great Dane with her incredible sense of hearing, in at least that respect, perceives things about the world I never will. Of course with my mind then same can be said of me in relation to her, but imagine a human mind with animal attributes and then imagine what such a creature would be like respective to either "root species."
Now, as far as the game and tradition and myth and even aescetics go, I can certainly see why some would object to such races based on their bizarre appearance alone (not to mention the fact that it seems to me more akin to science fiction than to nasty in many respects) and how that appearance all by itself would often be a cultural and societal defect, or at least a deficit. A needless one sometimes too. And I'm not real big on 32 different Player's Handbooks, 300 races, and 50 different classes. Core, or not. At some time you reach a definite point of diminished returns, not to mention a real degree of the absurd. There is such a thing as sensory and information overload and eventually even the most die-hard fan will say,
"how many different versions of a half-cat, half-goldfish, half-flying squirrel, war-forged, lightsabre wielding intelligent Giant Sloth with Bullette tusk armor and lizard clawed combat boots can you push out into D&D" before the ultimate 'cool-status' has been fully explored and extinguished. If I wanted that kind thing to go on forever then I'd just watch a rerun of
Giant Anaconda Versus Super Python XXII on the Sy-Fy Channel.
But despite the fact that I think the designers are intentionally writing their own created races into oblivion and obscurity in many cases by attempting to make each one cooler and more outlandish than previous races, I think that within these races lie the germinating seeds of something that are really and even intensely interesting. Like Chimeras. Like various psychological and physiological and even spiritual traits that would definitely effect how such "races" view the world, and interface and interact with it. As well as how they interact with others.
Now in myths the chimeras almost never successfully integrated with human culture. Or any cultures. They lived in the deserts and mountains and wildernesses by themselves, away from men. Like monsters, even if they weren't monstrous in behavior (Centaurs). There are both logical and pathetic reasons for such a state of affairs if you stop and think about it for just a moment. They wouldn't long feel comfortable around most people, and most people wouldn't want them in their taverns or agoras either. There would be exceptions of course, men who sought out the companies of chimeras like that, but most societies at large would see them as a threat, and that is perfectly understandable, especially when such creatures often possessed obvious physical advantages over most men and the best way you have to suppress or counter such uneven advantages are with daggers, swords, and wooden shields. Can anyone really doubt that Grendel, even if he tended to be a rather relaxed and good-natured fellow on most occasions would not be viewed at least suspiciously and warily whenever he showed up at the Mead Hall? Or that he would naturally avoid such places so as not to have to fight to the death some drunken fool who thought he could make a name for himself as the local Ogre-slayer? Of course men would be fearful of Grendel and of course Grendel would eschew the company of most men. He'd appear as a monster or demon to most, even if he possessed the golden heart of an angel.
However men with chimerical traits, from whatever source, beast or god, were often considered heroic, powerful leaders and often greatly admired. Herakles, Alexander, and so forth. Such heroes often also took on animal totems as emblems of their rank and capabilities. Because they were by nature part man, part divine, and part beast. Herakles wore the pelt of the Nemian lion, and so forth and so on.
So, all that being said, I have a suggestion and possible solution for those who don't like their character races running around looking like they are ready to butt heads in a mountain goat rally. Take such bizarre races, remove most of the physiological decoration and accoutrements, and instead make them into races which are basically humanoid in appearance, but still possessed of the rather amazing and interesting "capabilities" of the Dragonborn, the Tiefling, and others.
They can look like men or elves or dwarves or giants but they also possess dog-hearing, or eagle eyes, or maybe they can spit corrosive fluids, or maybe their blood is like ichor and is acidic (a giant would be a good play for such a character, as long as he is not so large he cannot adventure in normal sized environments), maybe they can absorb energy directly from the sun like a lizard, and so forth and so on. In this way they can fit-in to the general world and yet the players can still effectively explore the potential such characters would possess. All you would really have to do is transform physical appearance, traits could remain basically the same.
Or you could do it like in my setting. Chimeras have long figured in my setting because it is Byzantine and so in some ways the monsters and chimeras of the world are descendents of Greek Myth. When exposed to high level magics it will sometimes mutate men or elves or dwarves, etc. into creatures with new capabilities. It will create Chimeras out of them. Now sometimes this means the magics will make "monsters out of them" reshaping their appearance into freakish, bizarre, or frightening forms. So, in effect, you could have a man or elf reformed so that he appears like a Dragonborn or a Tiefling, and gains their capabilities. You don't really create a "new race" in this way, rather you create an individual Chimera, but you could use the race in the PHB as a template for what that chimera is like. (This would be analogous to a Marvel comic type mutant, different in both power and appearance to most men.) Or sometimes in my stetting a character's appearance will not change at all due to "magical mutation" but they will nevertheless gain new capabilities. You could use the PHB races as a "capabilities template" in that case. They remain perfectly human or humanoid in appearance in that case but are possessed of the capabilities of the other races. (This would be analogous to Superman, or Spiderman. Looks like a man, has the capabilities of a god or an animal) I think both approaches make for very interesting character types, because in the one case you have the obvious societal outcast, and in the other, the subtle outcast - he appears perfectly normal but is really a "stranger in a strange land."
But in either case you have two simple solutions.
1. Create new races merely by altering appearances so that these "new races" fit easily into your established milieu.
2. Create not races, but individual Character-Chimeras, that your players can play as a sort of add-on, or value added version of the new PHB races. And in this case they could either look human, or normal, or not.
Anyways that's my take on it.
Just because a Tiefling is drawn as a goat-headed, flaming-eyed, weird looking babe in the book doesn't mean she has to make an appearance in your world in that guise.
She could just be a normal looking gal who can see good in the dark, is hard to burn, consorts with demons, and has a mean, quick temper.
You know, you could just make her a red-head.
Well, maybe not that far, but I'm sure even 1e had some of these problems.
