Aliens with Human Appearance
There are several humanoid species in the Star Trek Universe that look exactly like humans. The unlikely fact that life on different planets has taken a similar, if not the same direction was sufficiently explained in TNG: "The Chase". In this key episode to the Star Trek Universe Picard's crew finds evidence that four billion years ago the first humanoid civilization explored our galaxy, and they were disappointed because they found themselves alone. To preserve their heritage, they spread encoded DNA fragments across many Class-M planets throughout the galaxy, thereby triggering a development similar to their own. Aside from the evolution schedule the DNA fragments, correctly assembled, contain a message to their descendants, namely humans, Klingons, Cardassians, Romulans and all the other humanoid races of the galaxy who are in some way related to each other.
As fascinating this theory is, a couple of problems remain. For instance, many alien species are indistinguishable from humans. Their appearance does not even show slight differences like facial ridges.
List of Aliens with Human Look
Indistinguishable from humans
The following species look exactly like humans, although they are assumed to have a different genetic background, aside from the kinship explained in TNG: "The Chase".
Very similar to humans
These species look like humans, but they have some distinct characteristics or abilities.
TNG: "The Chase" adequately justifies why most of the sentient lifeforms are humanoid. Yet, why do the countless above species look exactly like humans, whereas there is no second species akin to the Klingons, Ferengi or Cardassians? The Mintakans (TNG: "Who Watches the Watchers"), who are described as "proto-Vulcan", are the only explicit example of a prehistoric kinship of two non-human races, in an episode that aired three years before "The Chase". At that time it may have been the intention that "proto-Vulcans" are the descendants of an early spacefaring race that is the precursor of the Vulcans (and the Romulans likewise). This is in line with Spock's remark from TOS: "Return to Tomorrow" that colonization by Sargon's people may "explain certain elements of Vulcan prehistory".
It is obvious that human-looking aliens may help save make-up budget and time and that aliens with few make-up are easier to play by the actors. Lately, Voyager and especially DS9 have shown fewer of the "cheap" human look-alikes than TNG or TOS, as can be seen in the above table. Another practical explanation is that a race that looks like Klingons but is not Klingons would likely confuse even regular viewers.
Anyway, what is the fictional explanation? One theory may be that, similar as with the previous justification of the Klingon metamorphosis, the make-up technique or budget simply didn't allow to show all aliens the way they really look. Anyway, if we accept exactly how they look on screen, it is possible that some of the aliens are actually closer related to humans, and that they were abducted from Earth like Gary Seven's people (TOS: "Assignment Earth"), Miramanee's people (TOS: "The Paradise Syndrome") or the 37's (VOY: "The 37's"). However, it would have been noticed very quickly and should have been mentioned if aliens were genetically identical to humans. And why should some superior or early race kidnap almost exclusively humans and distribute them throughout the entire galaxy? Maybe they were human-looking themselves? Another solution is that humans might represent some sort of basic way that evolution most likely takes on an average Class-M planet and the other races developed under special environmental conditions. I don't like this idea because it's geocentric. It may facilitate the problem if we simply assume that most of the human-looking aliens have distinguishing marks and a different metabolism that is usually not visible.
Another point that alleviates the problem is that some of the less prominent non-human aliens look alike because of make-up re-use. In addition, many alien make-ups are so similar that they could be mistaken for variations within the same species. Especially in the three last seasons of Star Trek Voyager we see dozens of different races with not quite the same but very similar pronounced nose bones. So humans are not really the only species of which many clones or spin-offs seem to exist.
Another problem, however, is that humans easily seem to recognize each other although there are plenty of other species that look the same. Chakotay, for instance, saw that Riley Frazier was human at the first glance (VOY: "Unity"), and Janeway guessed that Seven of Nine was human (VOY: "Scorpion II"). In both cases the odds of meeting humans in the Delta Quadrant, even among Borg drones, were close to zero, and much rather they should have belonged to one of the many look-alike races that exist in the Delta Quadrant as well. Also, with so many human look-alikes and 150 member worlds of the Federation, why are human-looking Federation members and especially human-looking Starfleet crew members automatically meant to be Terrans (not to mention that most of the Terrans are Americans, as their names suggest)? So is it a certain smell or any other sense I haven't discovered yet (probably because I have met no aliens I could compare it with ;-))?
The predominance of human(oid) races is a concept useful to save budget and unpleasant hours in the make-up room, and to show facial expressions of actors playing aliens. We might have appreciated some more alien-looking species here and then, but TNG: "The Chase" eventually solved the basic problem. Personally, I don't mind that many aliens look exactly like humans. What bothers me more is that, while Terrans are dominating Starfleet anyway, all individuals that look human actually are human, except they live on some backward, isolated planet, like in so many TOS and TNG episodes.
Other Exobiology Inconsistencies - about humanoid kinship, evolution, "strong aliens", pon farr, Changelings, Klingon blood, etc.
Some screen caps from TrekCore. Thanks to LordKir for suggesting invisible distinguishing marks, to Doug for having a look at the close captioning concerning Ter(r)ellians and to Keith Thompson for the hint about Sargon's people in "Return to Tomorrow".