In “A Piece of the Action,” Jojo Krako said that he only saw 4 guys on the Enterprise, and maybe that’s all there was.
Well, I wonder if the Federation is like that. We know that there are Humans and Vulcans. And of course Andorians and Tellerites (and, of course the Iotians), but who else is there?
In the TNG era, Picard says there are more than 150 member planets, not including colony worlds. Presumably in Kirk’s time it was fewer, but certainly more than four.
The Coridians, I assume. 
Funny that, of the four founding member worlds, the show rarely shows Andorians or Tellarites, and virtually never in Starfleet. Andorians should be featured more prominently, they seem a very interesting race. Especially with those interesting antennas that can move thanks to cgi,
There must be some others. There was a shipload of delegates journeying to Babel, but none were mentioned by name.
There are a lot of Andorians in Enterprise.
Didn’t TOS starfleet basically have separate ships for the different races. The Intrepid was a Vulcan-only ship, and I thought it was mentioned that there were others. Enterprise was just a “human” ship that was willing to make a few exceptions.
While that would fit with what the Federation purports to be, I think the reality is that Starfleet is “humans only”, more or less. Every starship in Kirk’s time that was seen was humans in all the primary positions (Ultimate Computer, Tholian Web, Omega Glory). I don’t think humans trust other species to be in charge. And after the Intrepid loss, they may never be another chance.
Chauvinism: It is not logical, but it is often true.
In The Making of Star Trek (anyone who doesn’t have a copy ought to go out and buy one!), it’s said that the crew of each starship is made up primarily of one species, with a small sampling of aliens. The theory is that since they have more in common with each other, they will work more smoothly together and not require much in the way of different foods, day and night schedules, and so on. The *Enterprise *just happens to be manned by Terrans and the occasional alien.
(We all know about the Intrepid, manned primarily by Vulcans. In one series, I don’t remember which, wasn’t reference made to one manned primarily by Andorians?)
Watch Journey to Babel and count the number of species that sent ambassadors to the conference.
Don’t forget non-Terran humanoid members or prospective members like the Argelians, Zeons, Ekotians, Iotians, et al. Lotsa them scattered throughout the Galaxy!
I belive Kirk said to Zephram Cochrane that “We’re a thousand planets…” Even assuming some rounding up, I gather there are hundreds of permanent colonies and outposts in the TOS era, many of them settled by humans. Of course, it’s often unclear if a colony’s people are actually descended from Earth, even if they look outwardly to be completely human, i.e “The Cloudminders”.
I realizing TNG and later shows get a lot of flak for minimalist alien makeup, i.e. slap some headbumps on an actor and - voila! - an alien species, but TOS didn’t even have that most of the time.
TOS has big neanderthal guys! Guys so ugly they have to be kept in a box! They’ve got Tholians! They’ve got the Spectre of the Gun guys! They’ve got those hideous little puppet things in Catspaw! They’ve got Big pulsing brain guys! in Multiple episodes! One with actual pulsing brains!Gorn!! Andorians! Tellarites! The Salt Monster!
Post-TNG Treks idea of alien life is “If you leave the light on long enough it will become sentient”
I think even by the Enterprise era, Earth had expanded to Mars and maybe Alpha Centauri, and they’re the youngest race on the scene. The Vulcans and Andorians probably have at least dozens of colonies. It stands to reason that most races expand, at least within their own solar system, before making political alliances. The formation of the federation may have been a “merging of empires”.
Yeah, but how many of those guys are in the Federation?
And, you forgot Balok, The black/white, white/black guys, the Horta, and The Companion!
The Black/white, white/black guys are dead. As is the race of the Salt Vampires.
Though I’d love to see Balok’s people. They have some tech! But for all the series indicates, he might be the only one. Likewise the Companion.
I don’t think the Talosians are welcome in the federation. 
Could you imagine Horta in the federation council? Especially an angry one? “I must protest! The esteemed representative from the Horta just dissolved the Ambassador!”
Well, two of them aren’t. Or at least weren’t. They’d been doing their little cat-and-mouse thing for 50,000 years so who the hell knows how long they’ll live?
Anyway, looking down the TOS episode list for alien races that were outwardly indistinguishable from humans, eliminating the planets who may have been colonies of Earth (i.e. the native American transplants from “The Paradise Syndrome”) …
“Miri” is the first one with an entirely alien species that was not only indistinguishable from humans, they lived on a planet that was indistinguishable for Earth, for no apparent reason.
The “park manager” from “Shore Leave” looked human, but everything was fake so who knows?
The Metron from “Arena” looked human, but was clearly not.
The Beta III inhabitants (“The Return of the Archons”).
The residents of Eminiar VII and possibly Vendikar (I vaguely recall the latter was a breakaway colony of the former) from “A Taste of Armageddon”.
The Gamma Trianguli aliens (“The Apple”) had silver/grey hair but aside from the small antenna one of them had been implanted with so he could communicate with Vaal, they seemed indistinguishable from humans.
The tribes of Capella IV (“Friday’s Child”).
Whatever planet(s) Shahna and Galt and some of the others were from (“The Gamesters of Triskelion”).
The Iotians (“A Piece of the Action”)
The Hill and Village people of the planet Neural (“A Private Little War”).
The Zeons and Ekosians (“Patterns of Force”).
The people of Omega VI (“The Omega Glory”), whose “Yang” faction also has a fragmentary flag and constitution identical to that of the 20th Century United States, for no apparent reason.
The people of Magna Roma (“Bread and Circuses”) who also have a latter-day Roman Empire going, alongside nascent Christianity, and whose language has the terms “sun” and “son” as homophones by an astonishing coincidence!
The Sigma Draconis aliens (“Spock’s Brain”). The males encountered were bigger than the average humanoid, though not extraordinarily so, but the females were indistinguishable.
The Yonadans (“For The World is Hollow and I Have Touched the Sky”).
The Platonians (“Plato’s Stepchildren”) who had visited Earth and looked human but clearly had some variances, including extremely extended lifespans.
The Scalosians (“Wink of an Eye”).
The Gideonites (“The Mark of Gideon”), though they seem to have some additional regenerative abilities.
The Kalandans (“That Which Survives”).
The people of Ardana, both the Stratos and Troglyte cultures (“The Cloudminders”).
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In addition to the four in the OP we have Alpha Centauri which was a Founding Member. It was never made clear if there was native population with humans living there too or if it was just a human colony.
There a non-exhaustive list at Memory Alpha:
Just to nitpick…the Friday’s Child men are extra tall as are the white men in Elaan of Troyius,
Of course that also featured blue guys!
TNG should get a shoutout for Cardassians. I guess you could call them lizard or amphibian guys, but I thought they were very original.
And TNG had those fish guys. And let’s give a shout out to Riker for getting his freak on with an androgyne who…have husks inseminated to procreate??? I may be recalling wrong. There is a generally open minded guy! I think Frakes was willing to eat the maggots in Conspricy and kiss a boy in the aforementioned androgyne ep had one been cast.
At least i think he said so
Until “First Contact” I went with the TOS Technical Manual (Loved it!) that had Alpha Centaurians being nearly human and i went with the notion that Cochrane was from AC.
That’s nicely non-human centric if an alien nearby discovers warpdrive and helps Earth out.