Formionts are sentient stomach bacteria parasitising non-sessile life forms, modifying their hosts through a kind of nanoscale shapechanging. Human hosts become “vehicles” for formiont bacteria - essentially turning people into mobile formiont "cities" no longer themselves. (Which is the fate of the crew the PCs are seeking.) The act is neither good nor evil - it's just what formionts do. The "cities" communicate and interact through super-icky body stuff and transference of fluids which appear to humanoids like really horrific attacks, so it's quite tricky for the PCs to figure everything out.
I also really like Mike Ford's take on Klingons (from the novel The Final Reflection and the FASA Star Trek RPG; very different from how they wound up being developed in TNG and later canonical sources).
N'sss/Ravan from Star*Drive are pretty cool. They are cnidarian-like organisms that live in the atmosphere of gas giants. To interact with more robust species they use encounter suits, suits that can carry a variety of weapons if needed. One could compare their appearance to Daleks, but Ravan (their actual name) suits are ovoid and have multiple strong tentacles used for movement and manipulation. They also are one of two species that have mastered biotechnology within their social group and use modified parasites for a variety of tasks. One such parasite escaped their control and only works with them under duress of other species higher in the hierarchy. They aren't pleasant to interact with and probably would rather stick to themselves but have been absorbed into a religious group that uses their unique traits to manipulate outsiders. If they were freed from the Thaal, who knows what they would do.
Dralasites from Star Frontiers have already been mentioned but I think the Yazirians deserve a mention as well. Vaguely apelike but with a flying membrane like a flying squirrel, they can glide if the gravity is low enough and the atmosphere is thick enough. They also tend to go berserk in combat.
Man everyone took mine! I'd say all the alien species from 2300AD, they're all decidedly alien yet playable in a game starring humans. I also liked that all the aliens weren't magically advanced beyond humanity with the "mankind joins stellar species" trope. The Ebers are in fact a demonstration that an interstellar equivalent to the Twilight war is entirely feasible and should be a concern. Then there's the wholly enigmatic AGRA intelligence which is not playable but gives a nice object lesson that there's bigger things out there.
Traveller's aliens mostly felt to me like planet of hats aliens. The Traveller rules go nuts with world generation rules which result in crazy societies but when it comes to alien species it's just "oh, Aslan".
I liked Star*Drive aliens for the most part even though they mostly fell into the anthropomorphic alien trope. I think it's because they were intended to be PC species so they can't be too alien or else they're not playable.
Rifts Phase World had some cool species but suffer a bit from Palladiumitis in terms of playability. The concepts were cool.
It could be argued that, over time, players have been more willing or interested in playing more unhuman characters, while attempting to take them seriously. So Traveller aliens, due to their age, were aimed at a less exotic spot than Star*Drive and later games.