Twi'lek
'Twi'lek are one of the most iconic species in Star Wars Galaxy. These humanoids are entirely hairless aside from eyelashes (though many wear fake eyebrows) unusual enclosed "ears", a variety of bright skin tones 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.
Ryloth, their home planet, does not rotate. As a result of this one side is trapped in burning daylight and the other in night and freezing cold, leaving only the equator capable of sustaining life. Twi'leks did not develop space travel on their own, and often sold others or even themselves to acess the galaxy away from their terrible home. Compounding this further is the popular and naturally occuring drug Ryl, 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 for 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.
Star Wars RPG
Since this system didn't give much prominence to racial abilities, virtually any starting template that wasn't species specific could be 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 Dexterity, +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. 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 makes 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.
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.