Since their introduction to Star Trek lore in The Next Generation episode, “Q Who?” the Borg have been one of the Star Treks’ premier, and most dangerous, villains. Their cold and calculating drive to assimilate as many lifeforms as the galaxy holds is rooted in their desire to achieve complete and total perfection.
Although the Borg make a routine claim of “adding biological and technological distinctiveness to their own,” the truth of the matter is that the Borg don't seek to assimilate all species.
Would Assimilate - The Zakdorn
It’s not many species that can boast of having the most innately strategic minds in the galaxy, but the Zakdorn can proudly lay claim to that reputation. Captain Picard himself admitted as much in the Next Generation episode, “Peak Performance,” and the Zakdorn observer, Kolrami, proved it by beating Data in a game of Stratagema.
To say the Borg would be happy to assimilate the Zakdorn into their Collective would be a gross understatement. The tactical knowledge they could commandeer from this species would give them the edge in a battle with any foe.
Wouldn't Assimilate - The Pakleds
Quite quickly, the crew of the Enterprise-D realized that the Pakled’s deceptively simple speech patterns and feigned innocence masked a ruthless ambition that was evidenced by their kidnapping and torture of Geordi LaForge.
Based on those qualities alone, it may seem that the Borg wouldn’t mind adding that distinctiveness to the Collective, but chances are they would pass right over any Pakled ship. The reason? Pakled technology is a mish-mash of technology stolen from other races like the Klingons, Romulans, and Jarada. With their only redeeming trait readily available in countless other races and their technology falling suit, the Borg would ignore the Pakleds quicker than an Enterprise away team.
Would Assimilate - The Founders
The Founders are the shape-shifting heads of The Dominion, a conglomeration of worlds held under military rule in the Gamma Quadrant. Aside from gaining the advantage of espionage for their drones, assimilating The Founders would give the Borg literal control of an entire galactic empire.
The resources, culture, physiology, and technology of thousands of worlds would be at their fingertips, bringing the Borg that much closer to the perfection they seek. Additionally, the knowledge of science, species, and history The Founders possess would undoubtedly bring the Borg exponentially closer to conquering the entire galaxy.
Wouldn't Assimilate - The Son'a
The Son’a were the primary antagonists of the film Star Trek: Insurrection, and much like the film itself, were rather lukewarm villains. Eschewing the paradise-like planet that afforded them the gift of immortality for a life of trying to gather status and material wealth, the Son’a spent most of their time on cosmetic surgery.
Like a majority of filmgoers, there’s not much in the Son’a for the Borg to gravitate towards. Physiologically, the species is falling apart, requiring extensive surgery to keep their bodies together. Technologically, they’re not any more or less advanced than the next warp-capable species, so there’s little reason for the Borg to bother with the Son’a.
Would Assimilate - Species 8472
In a move that could be counted as one of the greatest blunders in Star Trek history, the Borg opened a portal into fluidic space and tried to assimilate Species 8472. Unfortunately for the Collective, this species was resistant to Borg nanoprobes and was able to do what Starfleet wishes they could have done: destroy Borg ships with almost minimal effort.
Despite the trouncing the Borg received from Species 8472, they remain high on the list of species the Borg would love to assimilate. Their dense biological makeup would add to the Borg’s imperviousness to biological and technological infection, making them an even deadlier force to be reckoned with.
Wouldn't Assimilate - The Kazon
The Kazon were supposed to be the new and formidable “Big Bads” that would plague Voyager for several seasons, in some of its best episodes, but turned out to be one of the most reviled species ever introduced to Star Trek canon.
As Seven of Nine once told Neelix, the Kazon were unworthy of assimilation and would have detracted from the overall perfection the Borg were chasing!
Would Assimilate - Humans
Since their first interaction and across several television series and one feature film, the Borg have done their best to assimilate humanity into their Collective. But like a poor marksman that keeps missing the target, the Borg have failed to add humanity’s biological and technological distinctiveness to their own, even after attempting to do it in the past when humanity was at its most vulnerable.
Undoubtedly, it’s that ineffable human quality to never surrender that the Borg wishes to understand and add to its Collective. Ironically, what the Borg are chasing is the very thing that proves that resistance isn’t futile.
Wouldn't Assimilate - The Ferengi
Envisioned as the primary antagonists for Star Trek: The Next Generation, the Ferengi were quickly relegated to comedy relief until Star Trek: Deep Space Nine painted them in a more compelling and favorable light. Still, the Ferengi were never known for their heartiness or bravery, instead garnering a galactic reputation for being unscrupulous and cowardly.
Reputation aside, there is little in the Ferengi for the Borg to wish to assimilate. Physiologically, they are fragile creatures and do not have traits that the Borg are interested in. Aside from a passing interest in their auditory capabilities, it's doubtful the Borg would assimilate the Ferengi.
Would Assimilate - The Q Continuum
It’s unclear if the Borg are even aware of the existence of the Q Continuum, a race of omnipotent beings who can literally do anything they wish at the snap of a finger. However, the Q are aware of the Borg, as it was the mercurial misanthrope himself who introduced the Federation to the Collective by launching the Enterprise into the path of a Borg cube.
The Q must represent the Holy Grail of assimilation targets to the Borg. All-knowing and all-powerful, an assimilated Q would represent the Borg having achieved God-like status, much to the chagrin of the entire Star Trek universe.
Wouldn't Assimilate - Tribbles
Tribbles are renowned in the Star Trek universe for being cute, (literal) balls of fur whose soft cooing can calm even the emotionless Mr. Spock. Yet the tribbles’ physiology hides a darker secret. As the Klingons figured out, a tribble’s propensity to consume exponential amounts of nourishment and procreate at an even higher rate can bring ecological disaster to any unsuspecting planet.
This may be interesting enough to the Borg to study with the ultimate aim being to create a biological weapon, but it is doubtful they’d assimilate tribbles, despite what any internet meme suggests. There’s simply no quantifiable benefit to the Collective in this trilling, furry puff-balls.