Hard to find a direct answer, but I turned up some candidates:
From the Wookieepedia page on species:
Some of the most prominent species in the galaxy were mammals, such as the Humans and their numerous offshoots, and the Duros. Other notable forms were Wookiees, Cereans, Bothans and Sullustans.
Reptilian sentient species were also very common in the galaxy, and notable examples included the Rodians, Barabels, Chistori, and Trandoshans.
From the Wikipedia list of species from Star Wars:
Humans are a race in the fictional Star Wars universe. They are the most numerous and dominant species, with apparently millions of major and minor colonies galaxywide.
From the uber-fan site Eleven-ThirtyEight, in a breakdown of gender demographics::
I have chosen to examine three of the most common alien species in the universe: Rodians, Twi’leks, and Zabraks.
From the same site's census of the species of every Wookieepedia entry for an individual character (as of August 2013, when the article was written):
In order to look at the demographics of Star Wars, it makes a certain sense to start by taking absolutely everything together – all characters recorded in all works. This fits with the principle of a single continuity that has so far governed the EU. Additionally, this information has already been recorded, in terms of ‘Individuals’ on Wookieepedia.
Wookieepedia records 22221 ‘Individuals’ at the current date. The same source recognizes the existence of 1825 sentient species. These species have a decidedly unequal representation. Firstly, only 553 merit their own category page in the ‘Individuals by Species’ organization. The remainder are presumably represented by a single individual.
Looking at the demography somewhat more deeply, there are very few species in the galaxy with any large number of individuals recorded. The following table compiles all such data (using the numbers provided in the ‘Individuals by Species’ categories, and including sub-species) for species with more than 100 individuals. Though this is an arbitrary cutoff, it is close to a level of 0.5% representation of the total number of individuals.
Number of Individuals
Percentage of Total individuals
Now, keep in mind that although this list was compiled in as scientific a manner as possible, it doesn't necessarily reflect the actual demographics of the galaxy. It reflects the demographics of characters prominent/popular enough to have both their own names and their own Wookieepedia pages.
Having said that, the ten most numerous species on the list, in order from most Wookieepedia entries to fewest, are as follows (I've added an example of each species for those who need it):
2. Twi'leks (Jabba's hot dancer)
3. Human clones
4. Rodians (Greedo)
5. Wookiees (Chewbacca)
6. Sullustans (Nien Nunb - Lando's copilot in RotJ)
7. Zabraks (Darth Maul)
8. Bothans (unseen spies who stole the Death Star plans for the Rebels in RotJ)
9. Transdoshans (Bossk)
10. Mon Calamari (Admiral Ackbar)
Here is the site's analysis of the numbers:
As can be seen from the above data the Human species is by far the most abundant, representing 42.6% of all individuals in the galaxy. The second largest group is the collective ‘Unidentified’ individuals, at 15.4%. Considering that this group surely includes a large number of Humans, the Human percentage of the total doubtless rises even higher. Ex. If Humans represent 42.6% of the ‘Unidentified’ category as well, then the actual Human # is 49.1%.
Additionally the Human presence is influenced by Human Clones, listed here as their own species and 2% of all individuals. I caution that the number for Clones is likely inaccurate, as the nature of wiki categories means many clones are also listed under rank and role categories such as ‘Clone Commander’ or ‘Clone Sergeant’ and may have been left out of the general categories, while other Clones may be double counted as both Human Clones and Humans. The clone numbers do provide a good example of source bias: they are obviously inflated by the emphasis in recent years on storytelling during the Clone Wars, which have massively increased numbers of clones present compared to any other period in the galaxy’s history.
Other species display similar forms of source bias. Ewoks, for example, appear only in a small number of Star Wars sources, but the vast number of Ewoks appearing on screen in Return of the Jedi and the two subsequent Ewok films, and the tendency to name every movie character in the Star Wars universe produces a very high Ewok number.
A mere seven alien [i.e., non-human] species are represented by 200 or more individuals. Bothans, Rodians, Sullustans, Trandoshans, Twi’leks, Wookiees, and Zabraks. Of these I find the numbers for Rodians, Sullustans, and Trandoshans the most surprising. Investigation of those species suggests that their numbers are heavily augmented by large numbers of NPCs recorded from the MMO Star Wars Galaxies. This suggests that species abundant as NPCs in Star Wars the Old Republic, such as Chagrians, Nautolans, and Togruta, may rapidly rise in individual number as more of that game’s lesser characters are added to Wookieepedia.
The finding that did not surprise me at all is that Twi’leks are, by a full percentage point or more than two hundred and fifty individuals, the most numerous alien species in the Galaxy Far, Far Away. I hypothesize that the reason for this abundance is the long-standing trend to utilize Twi’lek females as sexual symbols in Star Wars materials – a subject for a future column.
Some conclusions can be drawn from this demographic data. First, the number of species we see represented in the EU is extremely biased. The nineteen entries in the table above (removing the ‘Unidentified’ block) account for 61.6% of all individuals in Star Wars media (for now anyway, this number changes constantly, and is particularly subject to additions to TOR or new TV or movie material).
Second, the counts of individuals are dominated by visual media, particularly large cast video games (TOR has, to date, over 5000 characters, many of whom have not yet been given their own Wookieepedia pages). A key point of evidence here is the Yuuzhan Vong. Despite being more or less the only antagonist for a massive series of novels, there are only 121 named individuals. This is also supported by the relatively small proportion of Unidentified species individuals. Though 15% seems large, a great number of such species are drawn from purely written narratives, such as novels and prompts like the HoloNet News Reports series.
Third, we see a galaxy that is ruthlessly dominated by species in the ‘humanoid’ structural form. Out of those nineteen species only one, the Hutts, is non-humanoid. This probably won’t surprise any long-term fan of Star Wars, but based on these numbers it is probably not unreasonable to assume that less than 5% of all individuals in Star Wars media are non-humanoid.
Having quoted this article at some length, I feel obliged to explicitly credit its author, Michael Lind.
1 This post suggests that there are between 100 quadrillion and 400 quadrillion sentient beings in the galaxy. The problem with relying on Wookieepedia for our data is suddenly all too clear: We know that humans are the dominant sentient species in the galaxy; we know that there are at least 100,000,000,000,000,000 sentient beings in the galaxy, and a large portion of these must be humans; yet our figures list only 9,467 humans, less than one billionth of one percent of the total population.