Animals, especially mutant animals, come in lots of different shapes. Im going to dedicate this page to describing the various ways I have come up with to represent those shapes.
GURPS is a little strange in how it treats limbs. By default, you get the standard human allotment of 2 arms (with hands that have "enough" fingers and an opposable thumb) and 2 legs capable of moving you about at your default move (including jumping and swimming). There are various disadvantages that reduce that allotment or modify their capabilities, and advantages that add to it. How those interact however, is where the "little strange" comes in.
Limbs: GURPS gives back or charges points for capability. So long as you have the ability to move and manipulate objects as well as a human, whether you have 0, 1, or 2 arms or legs is a feature.
No Manipulators: A manipulator in GURPS is a limb, whether it is an arm or a leg. This disadvantage removes all your limbs (arms AND legs). You can still buy a Striker however, and Flight (Winged) still gives you a pair of wings.
No Fine Manipulators: This disadvantage transforms your hands into paws, at the very least. It can _also_ remove your arms completely, with no change in the number of points back (see the build for the Quadruped meta-trait as an example). Thus there is no separate "No Arms" disadvantage. Abbreviated here as NFM.
No Legs: This disadvantage/feature removes your legs. I call it out here because it makes explicit that having no legs but still being able to move normally (or at least, equivalently) is a feature. Inspect "Bounces, Rolls, or Slithers".
One Arm: This disadvantage is for beings with the ability to manipulate objects better than a paw, but with only one functional arm (denying the use of two handed weapons, etc). It is a step up from NFM. Adjust your hit location table to remove one arm (in a humanoid, make the arm a torso hit. In a Centaur, remove the roll to determine which arm is hit. Other morphologies need unique tables).
One Hand: Effectively buys NFM for just one of your arms. You have a limb with no hand: It gets Grip ST of 0.3xST in Technical Grappling, but doesnt count as an additional hand in Basic grappling, and can throw punches, or elbow strikes, as normal. Any random hit location result that indicates your missing hand will hit the arm instead.
Missing Digit: You have all your arms and hands, but one hand is missing some needed digits. A three fingered race that doesn't suffer any penalties to using their hands does not have this disadvantage. Rare in races, instead use Ham-Fisted or Bad Grip.
Bad Grip: You have all your hands and fingers, but you are not very good at using them. Also useful for modeling tentacles, beaks, and unusually dextrous feet. Applies it's penalty to combat, which is the major distinction between this and Ham-Fisted.
Ham-Fisted: You have all your hands and fingers, and can fight normally, but are otherwise poor at fine manipulation. Consider this the opposite of High Manual Dexterity. Useful for animals with good hands but lacking the neurological development for really good tool use.
Horizontal: This disadvantage interacts with arms and legs oddly. If you are horizontal and have 2 arms and 2 legs (rare), losing a leg causes you to fall down, even though you still have 2 arms and a leg to stand on. This is why Quadruped removes the arms (with NFM), and adds Extra Legs (4 legs). To keep your arms but avoid this issue, buy Extra Legs (3 or 4 legs) [5], and your built in Arms with (Temp Disad, 2 less legs -5%) [-1] or, if you have a lot of arms, some of which can be legs, buy Extra Legs (# of legs) [varies] and then your arms as pairs, each as 2 Extra Arms (Temp Disad, 2 less legs -5%) [19]. An odd arm-leg out gets the limitation but gets no points back.
Extra Arms: This buys you an additional limb with a fully functional hand. It can wield a weapon, punch, etc as normal. If it cannot, you can either buy Missing Digits for that arm (only if that is the only arm missing digits!) or buy Ham-Fisted and/or Bad Grip with the One Hand Only -80% limitation (from Martial Arts, p.42). Any tasks using the arm with Ham-Fisted or Bad Grip with other fully functional hands takes half the normal penalty.
Long: The primary cost of this enhancement it the bonus to swing damage. For arms that dont provide this bonus (long tentacles, for example), use Stretching or my Large Arm houserule.
Foot Manipulators: The -30% is for Legless. This is only appropriate if you remove all your legs while using your arms. Otherwise, buy your arms as described in Horizontal, above.
Weak: If your body is much stronger than all of your arms, each arm gets this limitation, and you should only pay full price for your ST up to your arms ST, buy the remainder of your ST with NFM -40%, as you can only apply your full strength as if you had no manipulators.
Striker: A striker buys you a built in melee weapon, mounted at the end of its own limb. This limb is used to represent damage to the striker itself, and should be treated as an arm without a hand for grappling purposes (0.3x Grip ST in Technical Grappling). Unless a striker is a horn or antler, it should not get all the benefits of a weapon, apply Damaged on Parry by Weapon -30% if it acts as an arm when parrying or being parried (for example, thagomizers or sticky tongues). Upgrading an existing limb so that it can make strikes uses the Limb -20% limitation on Striker. If you can cause damage with the striker at the same time as you use the limb normally (grabbing someone with a hand and hurting them with claws, like a crab), add Link +10% to both the limb and the striker.
Large Striker: This option is available for impressively large but not particularly long strikers. It doubles the weight of a striker, while also making it easier to hit by 1 per 2 levels (because this represents increases in density due to using horn or ivory over flesh, as well as increasing width instead of length). Thus, a Mooses enormous antlers, which weigh in real life up to 40lbs (for the pair, treated as one striker), start at 2.3 lbs (for ST 23), have Long and Large Striker 3, for a weight of 36.8lbs for parrying purposes, and can be targeted at +0 (-2 for limb, +1 for Long, and +1 for Large Striker 3).
Non-weapon Strikers: In my write up of strikers above, I include: Damaged on Parry by Weapon -30%, which means the Striker does not enjoy weapon like immunity to damage when it is parried by a defender with a weapon (give it DR instead) or parries a weapon itself.
Large Arm: This leveled perk increases the effective SM of one of your arms by +1, for purposes of what you can grab (while grappling, for example). It does not increase your reach (buy Long or Stretching for that), but does double the weight of your arm for purposes of parrying and being parried. It also makes your arm +1 easier to hit. Double the weight (and cost) of armor for that arm.
Long Neck: This leveled perk gives your Bite +1 SM worth of reach (only). It also makes your neck +1 easier to hit. Double the weight (and cost) of neck armor.
Not For Manipulators: As an alternative to the Weak modifier for arms: Buy any ST in excess of what all your arms can use with the limitation "Not For Manipulators -40%". This also limits the HPs that come with this limited ST, thus making your arms easier to cripple. This is especially appropriate for Centaur like creatures with strong legs and bodies, but more human-scaled arms.
Arms:
Almost Human: Many Monkeys and Apes have reasonably good manipulators. They have Ham-Fisted and possibly Prehensile Feet (above).
Long Tentacles: Most tentacles count as an arm with Bad Grip. I use Stretching to represent length however, as tentacles rarely provide the kind of extra leverage the Long +100% modifier on arms represents.
Crab claws: These are best described as an arm with Bad Grip, possibly with Large Arm. If the grip does cutting damage at the same time as it makes it grab (like a bite would), add Striker (Cutting, Limb -20%, Linked +10%) and Linked +10% to the Arm. Adjust the Striker with any or all of the Striker mods above, if it doesnt act as a full weapon (and in an animal, it shouldnt). A full build for a crab with one "Fiddler" arm:
Arms (Built In, Link +10%) [2] + 2x Striker (Cutting, Limb -20%, Link +10%, Damaged on Parry by Weapon -30%) [5x2 =10] + Large Arm 2 (Fiddler Arm) [2] + Bad Grip 1 or 2 + Arm ST (Fiddler Arm) [3/level].
Legs:
Prehensile feet: are Extra Arms (two arms; Foot Manipulators -30%; Short -50%) [4] (like on a monkey)
Dextrous Legs: without other arms (like on a bird) are Arms (Change built in arms to Foot Manipulators -30%; Short -50%) [-16], and add a Feature: No Arm or Hand hit locations.
Many, Many Legs: For things like Centipedes, I add another level of Extra Legs: 11 or more legs is 20 points and you lose -10% Move every # of legs/10 (round UP) legs you lose, to a minimum of 40% move at 1/3 your normal number of legs. Any further loss of legs causes you to fall, but you may still crawl with your remaining legs. The number of legs over 11 you have is a feature. Each leg requires over HP/10 to cripple, regardless of the exact number of legs you have.
Wings:
Flight (Winged) gives you a pair of wings which you can fly with. These wings are too delicate to hit someone with, even as a punch, nor are they useful in a grapple. This is useful for things like insect wings without carapace (dragon flies, butterflies, etc) but does not represent robust wings like those found on birds. Buy extra wings as if they where extra legs, reducing Air Move rather than ground move as you lose wings, though generally wings come in even numbers.
Bird Wings: Flight (Winged -25%; Temp Disad: No Strikers -6%) [28] + 2x Strikers (Crushing; Long +100%; Cannot Parry -40%; Weak -50%; Limb -20%; Damaged on Parry by Weapon -30%) [6]. This allows you to punch with your wings at Thr cr damage, and grapple with Grip ST = 0.3xST in Technical Grappling, but they provide no benefit in Basic set grappling.
Tails:
Tails are bought either as Strikers or as Extra Arms (or possibly both). The base advantage provides the additional limb. Tails that are too big to hide under abdomen armor but cannot manipulate objects or make useful strikes are a Quirk, and are attacked as an extremity (-3 (not -4) to hit, over HP/3 to cripple). Tails that can be hidden under abdomen armor and are otherwise useless are a feature, and are attacked as an extremity (-4 to hit, over HP/3 to cripple).
Thagomizer: As seen on a stegosaurus or anklyosaurus. Named after the late, unfortunate Thag. This is a Striker (Crushing, Cutting, or Impaling; Cannot Parry -40%, Damaged on Parry by Weapon -30%). Often, these are not flexible or long enough to reach in front of the animal, and so get Limited Arc (Rear), often with Clumsy.
Scorpion Tail: As a Thagomizer, above, but Impaling, Limited Arc (Front) and no Clumsy. Poison is a follow-up, as normal.
Monkey Tail: A prehensile tail is Extra Arm (Extra-Flexible +50%, No Physical Attack -50%) [10]. Rarely, these are strong enough to remove No Physical Attack, possibly replacing it with Weak. Add Bad Grip 3 (One Hand Only -80%) [-3].
Normal Tail: Most normal tails are just really bad strikers: Striker (Crushing; Cannot Parry -40%; Clumsy -20%; Limited Arc- Rear -40%; Weak 1/4 ST -50%; Damage on Parry by a Weapon -30%) [1]. This can matter for very large animals, who can still deliver a dangerous strike with their tail, even if it is weaker than a kick or shove.