From A Wiki of Ice and Fire
Palanquin is a litter, a class of wheel-less vehicle for the transport of persons.
References in the books
- Daenerys Targaryen, her brother and Magister Illyrio travelled in Illyrio’s elaborately carved palanquin on the way to present Daenerys to her prospective husband Khal Drogo. The streets of Pentos are pitch-dark when they set out so servants go ahead to light the way, carrying ornate oil lanterns with panes of pale blue glass, while a dozen strong men hoisted the poles on their shoulders.
- While in Vaes Dothrak pregnant Daenerys Targaryen opts to be carried in a litter to visit the Western Market. If Khal Drogo were accompanying her she would have ridden her silver not wanting to appear weak in his eyes but with her husband off hunting she finds it pleasant to lie back on soft cushions and be carried across Vaes Dothrak, with red silk curtains to shield her from the sun.
- The Prince of Pentos rides about the city in a palanquin of ivory and gold. Three heralds go before him.
- In Asshai those who dwell there often ride in palanquins of ebony an iron, hidden behind dark curtains and carried upon the backs of slaves.
- In Volantis it is said that travelling afoot can taint visitors in the eyes of foreign born captains and the Volantenes alike, therefore persons of quality travel by palanquin, or in the back of a hathay.
- After being refused by the Pureborn Daenerys Targaryen rides in a palanquin pulled by bullocks with Rhaegal and Xaro as Jhogo clears a path. The drapes kept out the dust and heat of the streets, but they cannot not keep out disappointment.
- Daenerys chooses to ride the silver for her visit to the docks of Qarth. She rejects going by palanquin, feeling she had reclined too long on its satin cushions. 
- At the kingsmoot, Erik Ironmaker, called the Anvil-breaker, was carried on a palanquin by three of his grandsons.
- Yurkhaz zo Yunzak comes and goes in a palanquin so huge it requires 40 slaves to carry it.
- Tyrion Lannister is smuggled out of Pentos inside the litter of Illyrio Mopatis, they travel in it on their way to the Rhoyne. It is suspended between eight mammoth draft horses on heavy leather straps. Four eunuchs pace beside the horses. Two on either side, and more trudging along behind to guard the baggage train. Inside it is pleasantly warm, despite the autumn chill.
- A matron on an antique palanquin bids on Tyrion Lannister and Penny when they were up for sale on the slave auction block outside of Meereen.
- The Meereenese seldom ride within their city walls. They prefer palanquins, litters, and sedan chairs, borne upon the shoulders of their slaves. A man of Zakh tells Dany that horses befoul the streets, slaves do not.
- For Daenerys Targaryen's wedding procession in Meereen Reznak ordered that her palanquin be made ready. Daenerys thinks that it is too hot for that mode of transport. Nor does she wish to go to her lord husband upon the backs of bearers. She instead chooses a sedan chair. 
- Daenerys and her husband Hizdahr ride in an ornate open palanquin on two thrones side by side, surrounded by Brazen Beasts on their way to Daznak's Pit.
A palanquin fit for a man of my stature.
- Tyrion Lannister's thoughts as he is nailed into an empty wine cask.
References and Notes
- A Game of Thrones, Chapter 3, Daenerys I.
- A Game of Thrones, Chapter 54, Daenerys VI.
- A Dance with Dragons, Chapter 1, Tyrion I.
- The World of Ice & Fire, Asshai-by-the-Shadow.
- A Dance with Dragons, Chapter 6, The Merchant's Man.
- A Clash of Kings, Chapter 40, Daenerys III.
- A Dance with Dragons, Chapter 48, Jaime I.
- A Clash of Kings, Chapter 63, Daenerys V.
- A Feast for Crows, Chapter 19, The Drowned Man.
- A Dance with Dragons, Chapter 47, Tyrion X.
- A Dance with Dragons, Chapter 43, Daenerys VII.
- A Dance with Dragons, Chapter 52, Daenerys IX.