Twi'lek

Twi'lek are one of the most iconic species of the Star Wars' Galaxy. These humanoids are entirely hairless aside from eyelashes (though many wear fake eyebrows), posses unusual enclosed "ears", come a variety of bright skin tones (though blue is most common) and, most importantly, have two tentacles protruding from their head called lekku. Lekku contain part of the Twi'lek's brain, are sensitive to the touch, and capable of articulation to the point they have their own sign language. Two Twi'lek appeared in relatively prominent roles in Return of the Jedi: Jabba's Major Domo Bib Fortuna and Jabba's slave dancer Oola. The early expanded universe followed this by introducing several well received major Twi'lek characters like Nawara Ven - a clever (and surprisingly moral) lawyer turned fighter pilot, and Boc Aseca - an insane dual wielding dark Jedi, on top of many background appearances. While Bib Fortuna had the larger role by far, Oola gained prominence as the only remotely "sexy" alien (indeed, the only young female of remote prominence aside from Leia) in the original trilogy, and most female Twi'lek take after her. Unlike many clones of movie characters in the expanded universe, there's actually a good explanation for this. Later notable Twi'leks include Jedi Master Aayla Secura and Sith Lord Darth Talon, the two most Rule 34:able characters in all of Star Wars.

Ryloth, their home planet, does not rotate. As a result of this one side is trapped in burning daylight and the other in freezing night, leaving only the equator capable of sustaining life. Even then the equator is often full of badlands and subject to powerful heatwaves. This limited space and harsh environment forces most of the population in giant, elaborate, underground cities. Twi'leks did not develop space travel on their own (Natural, as flight on its own isn't much use when you live underground), and often sold others or even themselves to access the galaxy away from their terrible home. Compounding this further is the popular and naturally occurring drug Ryll, which is mined on their home planet and constitutes their only other export. This attracts a lot of criminals and ensures any anti-slavery crusader would destroy Ryl'loth's economy. Finally they are physically about as far away from the center of the galaxy as one can, being end of the line of the Corellian Run hyperspace highway, and located in the loosely controlled and crime friendly Outer Rim.

Due to their prominence and fandom, Twi'lek naturally appear as playable race in all Star Wars RPGs to date. Indeed, as with many things Star Wars, the West End Games splat was to first source to give their proper name and basic background.

Star Wars RPG

Since this system didn't give much prominence to racial abilities, virtually any starting template that wasn't species specific could put Twi'lek as species and be done with it. One Twi'Lek specific template, Twi'lek Co-Pilot, was introduced in Platt's Smugglers Guide. It's a pretty typical rogue template, though it did give them the lekku "language".

Star Wars D20

Twi'lek appear in the core rulebook and have the following racial traits.

+2 Charisma, -2 Wisdom (The wisdom penalty is likely based on Bib Fortuna falling for Luke's mind trick, marking him as weak willed)

+1 fortitude saves

Low-light vision

Yeah, most non-Humans in Star Wars D20 got the short end of the stick.

Ryloth is detailed in Geonosis and the Outer Rim. While many other EU encyclopedias detail the planet, this is one of the few sources for the mundane day to day life on the planet.

Saga Edition

Twi'lek once again appear in the core rulebook with the following racial traits.

+2 Charisma, -2 Wisdom

Deceptive: Naturally gifted at manipulation, a Twi'lek may choose to reroll any Deception check, but the result of the reroll must be accepted even if it is worse.

+2 to Fortitude Saves

Low-Light Vision

Saga Edition doesn't hate non-humans and Twi'lek got off pretty well. The bonus to fortitude doesn't actually have an equivalent feat for non-Trandoshan (nearest is +1 to all saves) and is quite useful because of Saga's damage threshold system where if you take more damage than your fortitude save from a single attack you get a wound. Their wisdom penalty means that they get one fewer force power every time they take Force Training (and since extra uses were done with duplicate powers, fewer uses per encounter), though the few powers they got were are more powerful. Since several Twi'lek Jedi were prominent in the Expanded Universe (one enough so George Lucas added her to Attack of the Clones) this would be rectified in Rebellion Era Campaign Guide with the Twi'lek only feat Jedi Heritage which adds four to their effective wisdom for gaining force powers. This gave Twi'lek force power specialists the best of both worlds and gives them a lot of (uses of) force powers. Since many game (including Dawn of Defiance) are set during the Empire, a bonus to deception is useful in even the most goody two-shoes group.

Star Wars Roleplaying Game

Twi'lek are printed in Edge of the Empire and Force and Destiny core rulebooks (for some reason they aren't in Age of Rebellion, though as all systems use the same rules porting them is a non-issue). They have the following racial traits.

1 Brawn, 2 Agility, 2 intellect, 2 cunning, 2 willpower, 3 presence (essentially +1 presence, -1 brawn)

Wound Threshold: 10 + Brawn

Strain Threshold: 11 + Willpower

Starting Experience: 100 XP

Special Abilities: Twi’leks begin the game with one rank in either Charm or Deception. They still may not train Charm or Deception above rank 2 during character creation. When making skill checks, Twi'leks may remove ■ imposed due to arid or hot environmental conditions.

Twi'lek are... OK. Brawn is mostly a dump stats for anyone not planning to enter melee or use heavy weapons since it just determines starting wound threshold (HP) that's quickly dwarfed by talents that boost it. A lot of prominent outer rim planets are big dead rocks, volcanic, or hot jungles, so the environmental ability is more useful than you'd expect in Edge of the Empire.

The problem for Twi'lek is that they are focused on Presence when Presence is, like most Charisma stats, largely wasted if you aren't in a career (class) or specialization (subclass) that focuses on it since it boosts some (but not all) social skills, and a skill that recovers strain (non-lethal damage) at the end of an encounter and determine initiative when you ambush someone. To make this worse most of those are in Age of Rebellion while Edge of the Empire has one specialization in its core book that uses charisma while having social skills in class. In Force and Destiny the Makashi Duelist tree lets you use presence to swing a lightsaber, but it's (per Star Wars canon) focused on lightsaber duels which will happen a few times in your character's lifetime and is in a different career (Mystic) from the most Presence focused specializations (Guardian's Peacekeeper).

Monstergirls

Like Elfs, Twi'lek are subject to the question "are humanoids drawn as the normally are, just with (even) less clothing, actually monstergirls?". Sexy alien girl is a pretty vanilla, if stereotypically nerdy, porn target. Twi'lek are sex symbols in Star Wars canon so porn is obvious. Since Lekku are both prehensile and sensitive to touch, even the most remotely deviant thing about them pretty clearly exists within the context of the setting anyways.

Interestingly, Lucasarts officially published Star Wars Art: Visions, which contains multiple pieces of lewd Twi'lek art. Sure it's officially "artistic" nude, but it's still official art of Twi'lek nipple. George Lucas himself may approve of sexy Twi'lek girls, as both Aayla Secura (A female Jedi who he liked enough to add to Attack of the Clones) and Darth Talon (a female Sith lord that wears pretty much nothing) were praised by him on their appearance alone.