With all the various races in the federation, how do the humans manage to dominate it?
While Enterprise addresses some of this issue, it's largely unexplained in the Star Trek universe. Of course, it always helps in story telling because aliens characters are sometimes more difficult for viewers to relate to than human looking ones.
In some episodes, the viewers are led to believe that there are other ships where the crew is primarily Vulcan or some other race. But it is rare that a non-human Star Fleet captain is an important character in an episode.
In Enterprise, the adaptable humans are often contrasted with the rigid Vulcan race or the passionate Andorians. In that series humans are the crucial peace-makers that bring about a new universal order, if you will, in the form of the Federation. Basically the humans represent a middle of the road species with a recently made Utopian society that allows them to more easily negotiate peace between different species (Vulcans and Andorians). Because humans are at the center of the creation of the Federation, we are led to assume that Earth is a primary recruiting world for service in Star Fleet.
Star Fleet was mostly human in the Original Series, but the Animated Series had a wide variety of non-human crew members. I think that it was just too much of a make-up, acting, and story-telling challenge to have too many regular non-human characters in the live-action show.
We are never given a single, canonical reason why this should be so. Some of the novels (mainly Diane Duane's) have postulated an alternate view in which even Enterprise is not dominated by Earth-descended humanity, but a fully integrated crew of many species, but on-screen, certainly, even the 2009 movie shows a predominance of humans in Enterprise's crew.
Star Trek: Enterprise implies that the lessons that humanity learned from its wars that allowed it to unify after First Contact made it an ideal catalyst for bringing the various other races in its region of space together (e.g. Vulcans, Andorians, Tellarites), and of course, puts much of the credit on Captain Archer and his crew.
The early stages of the Original Series don't really talk about the Federation, and in fact leave it quite vague under what authority Enterprise (1701) and Starfleet operate. "The Cage" for example implies that Enterprise is an Earth vessel, not a "Federation" vessel, and other early stories continue this implication. This makes Spock's presence even more remarkable, since in this conception, he really is the only alien on the ship!
Over time, the concept of the Federation evolved, and although the classic series would never show any other aliens on Enterprise, it would mention an all-Vulcan-crewed starship, Intrepid, with the implication that other major races probably had either their own separate fleets, or their own ships with crews predominantly of their race. It isn't until Star Trek: The Motion Picture, in the big Rec Deck scene, that we begin to get the sense of greater inter-species integration in the crew, suggesting perhaps an in-universe explanation that Starfleet was nervous about different species cooperating closely on that level without rivalry and chose to integrate slowly.
In the end, however, for all that he got down-voted, @vonjd above is not incorrect. Roddenberry's vision was about the human future, and for good or ill, it took later writers to run with the idea that, if humanity could learn ignore skin tone and religion and gender, it could also crew a ship or station with other species on board.
There's also a purely practical issue, which is that the makeup to create most of the alien viasages is expensive and uncomfortable to wear. Michael Dorn's skin was profoundly affected, for example, by years of wearing Worf's bumpy head. Susanna Thompson (who played the Borg Queen in several episodes of Voyager) almost quit after the first day of filming because she found the makeup and costume so painful to work in. Today, with modern CGI, it might be possible to crew Enterprise with some of the more interesting non-homonid races Diane Duane cooked up, but it would still be an expensive prospect.
[Update 16 April 2019: Star Trek: Discovery has retconned and reinterpreted the 2250s somewhat. The operating authority of Starfleet has now been established to be, and to have been, the United Federation of Planets as we came to know it. The various Starfleet ships we see have a much more "mixed" crew, more akin to what Diane Duane used to present in her books, because modern budgets and make-up capabilities make it possible, although we still have not seen anything quite so alien as a Hamalki turn up.
We also see some evidence that the Admiralty is more explicitly mixed. Generally, when we see more than one admiral in Star Trek: Discovery, we see representatives of the Founding Four--humans, Vulcans, Tellarites, and Andorians.
None of which changes the overall sense that humanity, and Earth, are "senior partners" in the Federation, which leaves the original question still valid, and still canonically unanswered.]
Humans in the Star Trek universe are expansionistic, not self-destructive, and breed easier than similar species. The other 'main' races of the Federation, the Vulcans and the Andorians, have severe limitations on their reproduction.
Vulcans only enter pon far once every seven years, and the Andorians require four parents for a successful pregnancy. This has gotten so bad for the Andorians that they have a serious population issue - their numbers are shrinking.
We don't see much of other non-human species - there aren't many represented on the ships or stations we frequently see. It's therefore likely that other species don't have the same drive that humans do to 'seek out new life and new civilizations'. Humans likely make up a significant percentage, perhaps even a majority, of Starfleet.
With humans as a driving force behind Starfleet, and populating a significant number of the Federation's planets, the bigger question is "How could humans NOT dominate the Federation?"
It bears mentioning that their enemies aren't much better off when it comes to population or reproduction:
Romulans have largely the same limitations as Vulcans with the added detriment of a society that does not encourage love, trust, or mutual support.
Cardassians don't have any obvious difficulties reproducing, but they are hampered by their society. It tends to be repressive, and morale (and therefore, birthrate) of its population suffers.
Klingons are violently self-destructive. From the time they enter adulthood (prime reproductive age) their warriors seek violent deaths, and all too often find them.
And it's important to note that "Star Fleet" was in existence before the creation of the Federation, which would set the tone for the culture of Star Fleet. In the 1960s, the parallel to the Star Trek Earth was of course, the United States. The UN is located in New York as the Federation was located on Earth and at that time (and still, for that matter), the U.S. was generally the Big Stick for various confrontations around the world.
The interesting question is this: In TOS, there were rarely more than shuttles or small transport ships from other species within the Federation. Are we to assume that the Vulcans, Andorians and Tellarites disarmed and dismantled their capital ship fleets?
I think that what we see is one factor that leads to a two-pronged disparity:
Humans are explorers.
I think that's the reason. When First Contact occurred with the Vulcans, the Vulcans were still pretty much sitting at home, with occasional science expeditions every now and then.
But when humans took to the stars, they really started exploring. This has caused two things:
They have gone to terraform other planets and live on other worlds, because they love the sense of adventure that colonizing brings.
While all members of the Federation can join Starfleet and explore the world, not as many do, because they don't love to explore as much.
So, the reason there are probably more humans in the Federation, because they're living on many more worlds, and humans are more likely to join Starfleet than other species. This compounding factor means there are a lot more humans in Starfleet than other species. Sure there are a few token Benzites here and there, but not as many.
Whether humans "dominate" the Federation is unclear. The head of the Federation has been shown as a non-human twice in Star Trek history (Jaresh-Inyo, a Grazerite, and Ra-ghoratreii, an Efrosian) and human twice (Jonathan Archer and Hiram Roth). This is too small a sample size to draw any solid conclusions about the ratio of human to non-human presidents, but it does indicate that the head of state isn't always human (as would be expected given the democratic nature of the Federation).
It's also been suggested in at least ENT, TNG, and DS9 that there are many non-human and non-Earth-based starships in starfleet. While integration might be preferred given the goals and ideals of Starfleet and the Federation, there are practical advantages of having a crew that is mainly comprised of species from a single world:
- The physiology of different species can vary greatly, and their environmental as well as ergonomic needs are different. It would be easier to crew starships with lifeforms that have compatible environmental needs and who can be accommodated by a shared ergonomic design of equipment.
- Species that already live on the same worlds are accustomed to living and interacting with one another. Cultural differences are therefore less likely to come as a surprise or interfere with teamwork. Sharing a common thread can also bond the crew and strengthen comradery.
- It's just more convenient to have ships based in Earth to be crewed primarily by inhabitants of Earth. The same would be true of starships based in other planets.
As for why Earth is the leading member (and in effect the capitol) of the Federation, that comes down to Earth being one of the founding worlds and the one that, as Mark Rogers points out, was the peacemaker that really brought all of the founding powers together to begin with.
So the bigger question is, why isn't Earth a more integrated society? Given the Federation's aims and ideals, you would expect to see lots of cross-species immigration between Federation member worlds. However, the only planets that seem to have integrated populations are Risa, a resort planet of the Federation, and Farius Prime, a neutral world that is in the lawless borderlands.
Humans aren't the center of the Federation, other than Earth being where the Federation is headquartered.
The main reason that most of Starfleet is human is simply because Starfleet is what the Earth Starfleet (which was a Terrans Only Club) evolved into, meaning that most other races didn't have the same incentive or ties to it as Humans did.
As for the Federation itself, the only time we see the Federation's President as a Human is in The Voyage Home, where as in The Undiscovered Country the president is an Efrosian, and in DS9 the president is a Grazerite.
There are many races in the Star Trek universe that are so near-human there may be no discernible difference. The Betazed and the Trill (unjoined at least) are all indistinguishable from human on their exterior, just to name a few.
It's also very likely that humans, with their appetite for colonization, would have spread to nearby systems that didn't have an intelligent race living on them. This is borne out time and again in space sci-fi; whether humans have supralight travel or not, they've usually colonized Venus, Mars, Io and other gas giant moons, and built orbital stations around gas giants and "deep space" stations in areas without a solar system but with strategic significance. If they can live there, they can live anywhere.
I always thought of it like the United Nations in a way, each planet has its own protective force (i.e. Betazed only had defense satellites and was taken over by the Dominion, and Vulcan never had anything but a science fleet) and when the federation was formed Earth gave its space institute up along with its self governance to become the capital world (so it's protected by Starfleet). They do mention the problem is, at least to some level, integration of the member militaries (could be explained that planetary defense is security not military), but then you would think there would be a few ships that look more Andorian or Vulcan like a modern Surok class or something in Starfleet.
I think its a mix of all these......star fleet is an earth organization so it would make sense that earth(probably the largest human population) would recruit more humans and on other worlds there most prominent institution would not have many aliens to there world in it, its kinda implied that people can study to join starfleet anyplace but to get commissioned or enlist you have to go to star fleet acadamy on earth and pass certain criteria, also humans can breed like crazy and we are extremly expansionist and dont know how i got this idea but I always thought it was clear that humans are better suited to the difficulties of space travel so it took longer to accommodate other species, I'd say the bigger question is about ships and that one really was money issues(cant built cheap realistic models without cgi) as if you watch tng and ds9 they reuse the wedge ship dozens of times for a wide range of species.
Humans dont dominate the Federation in fact I dont think we have ever seen a human President on screen and we see many different species scientist's and Ambassador's in Tng and DS9. Humans do dominate Star Fleet and that would be because its a human founded Organization on the home planet of humanity....just like the vulcan science academy is dominated by Vulcans but aliens do go there.
You're all wrong. Starfleet Academy is like the West Point of Star Trek. And to be an officer on a Starfleet ship, you have to graduate from Starfleet Academy. That's why in shots of the Academy, you see mostly humans with a small scattering of aliens.
There are similar institutions with similar standards of admission on other planets, like the Vulcan Science Academy which also graduates a lot of top level officers. And other planets have their own "Starfleet" equivalents. It makes sense that Earth ships would have mostly humans, Vulcan ships would have mostly Vulcans, etc..
The people making Star Trek would have liked to show all these diverse beings on different ships, but the cost, makeup, and even CGI are prohibitive.