There are quite a few RPGs available where you can play a non-human race (or alien). Outside of the RPG realm, it also has a significant presence in books and shows (the latter more in sci-fi shows/movies). However RPG games like A Song of Ice and Fire (based on novels and then a tv show), Serenity (based on the TV show and then movie), and the MechWarrior/Battletech universe all suggest you can have a just fine role-playing game without needing additional races.
So the real question is: what do non-human races (or aliens) add to a RPG setting? Without races, you can still have plenty of differentiation based on cultures — the difference between cultures alone in Asia is enough to prove that. Indeed, at the start of races (dwarves and elves for example), it usually starts with a culture that could just as easily be based on humans as it would be on the non-human races. A setting typically tries to take that a bit further and create something unique to the races that cannot be based on just a people living underground (dwarves) or in forests (elves). For the latter, they start to factor in how their culture and world-view is shaped by their long-lives.
However, a long-lived elf has a much different sense of urgency than say a human, which is both a source of strength and a failing in say Tolkien’s Middle Earth. The history of the elves in Middle Earth is shaped by the fact that the elves take a long-view on things. However, watch the movies and you can see that Legolas is very human in his views on a large amount of topics — the only thing that diverges is his abilities are significantly different than a human.
One of the better takes on what it would mean to be a long-lived race, is actually in the Vampire games by White Wolf. Non-player character vampires almost always take a long-view on schemes and plans, because they have all the time in the world once they deal with feeding to keep in their current state. So what would a world populated by a long-lived race such as elves? They could easily obtain a subtle sort of power to influence shorter-lived races kingdoms.
Think about it. The Roman Empire started in 27 BC. After it split in 330 AD, the Western part of the empire lasted until 476 AD, and the Eastern part of the empire (more commonly called the Byzantine Empire) held on to 1204 AD. It was re-founded in 1261 and lasted until 1453. Taking the Western Roman Empire, it lasted about 5 centuries. An average elf in third edition D&D can live up to 750 years (the average looks like it would be around 570). So it could be totally plausible if the passing of an elf or group of elves lead to the decline of an empire because the founding vision behind the people who did the heavy lifting suddenly were gone?
At that point, the question becomes, how to adequately role-play a long-lived race? The urgency and their goals would be significantly different than a shorter-lived race like humans. Bandits plaguing a small area are a short-lived nuisance. They will likely be dead of old-age prior to 40 years passing, so there is really no need to deal with the problem … it will go away on its own. That attitude doesn’t really make great heroes of a traditional sense, so how to mix that character into a group of shorter-lived races would be really tricky.
I digress though. The real crux of the question is simply this … if you are portraying non-human races as basically humans with different abilities, why not have the different abilities as classes (or packages or whatever) and just build cultures around what were previously different races?