Alien life can take all sorts of shapes and sizes. When it comes to the various flora and fauna of other worlds, there’s no limit to where your imagination can take you.
But, when you start talking about intelligent, civilized, technological aliens… then you need to have some limits. Specifically, in terms of physical form. For a species to reach the stars, they have to have the capacity to create the means to do so. So your intelligent, star-faring species HAS to had a similar physical capacity: able to dominate its ecosystem enough to acquire its caloric needs and survive to reproduction, and with the fine motor necessary to build simplex and complex technology.
So, on some level, I am fond of going to the Humanoid shape: humans are unique on this planet in that they are the only species that can run a mile, swim a mile, climb a tree and throw a rock, let alone do calculus, build microchips and post on Facebook. It’s highly functional and adaptable. Is it the only one? No, but don’t dismiss it. Yes, most shows and movies went to the humanoid well most of the time for aliens, but that was mostly because actors who are otherwise are notoriously unreliable in learning their lines.*
Some other forms that I use, as a basis for alien building:
Bipedal: Technically different from “humanoid”, which implies two legs, two arms, a body trunk and a head on top. “Bipedal” just beans two legs, and the rest of the design might be quite different. It should, however, maintain bilateral symmetry.
Tripedal: Three legs, and I usually have this also mean three fine-motor arms as well, if not full on trilateral symmetry.
Centauroid: Four legs, two grasping arms. Sometimes I might use “Insectoid” for this form as well, if the two grasping arms double as walking limbs.
Quadruped: Four legs. Now, you still have to deal with fine motor control. Two or all four legs might double as fine-motor graspers. Or there might be another method: the Zaaatel are catlike creatures with strong cilia-like tentacles coming from their spines. A quadruped could also have eight limbs: four walking, four grasping.
Hexaped: Similar to the “Insectoid” or “Centauroid”. I might use this instead of “Insectoid” A. if the species didn’t have a chitonous exoskeleton and B. if all six limbs were walkers and graspers.
Arachnoid: Eight walking/grasping limbs.
Medusoid: Snake-like body with two grasping limbs.
Centepecoid: Catch-all for any segmented-body with more than eight walking/grasping limbs.
Tentacloid: Catch-all for any species that has multiple tentacles for both locomotion and fine manipulation. This can vary: the Starkasians have three large-body-trunk tentacles for locomotion, and six fine-motor ones for manipulation. The Calitras are Winged Tentacloids, with twelve fine-motor tentacles for maniuplation, and wings for locomotion.
Any other important shapes you think I might have missed? Let me know.
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*Farscape, and to a much lesser degree Babylon 5, tried to avoid this somewhat with puppets. Farscape, being a Jim Henson Studio, succeeded with this to a far greater degree.