In the books
In the A Song of Ice and Fire novels the islands are called Sweetsister, Longsister, and Littlesister. The islands are ruled by the houses Borrell, Longthorpe, and Torrent respectively, although the archipelago as a whole is ruled by House Sunderland (though the exact location of House Sunderland's castle-seat is not clear). People from the Sisters are known as "Sistermen". Some of the lords of the Sisters are rumored to have webbing between their hands and feet, which is true at least in respect of the Borrels. "Sister's Stew" is a noted dish popular on the islands.
The islands are noted for their roughness. They are popular with smugglers, traders, and sailors, but are considered to be dens of avarice and sin by septons. The Three Sisters were too small to resist outside conquest and become a regional power in their own right, and thus are regarded as mere pirate dens. In contrast, the Iron Islands raided surrounding lands by sea but were larger and strong enough to be an independent kingdom, so their "piracy" was enshrined as a cultural institution, "paying the iron price".
About two thousand years ago the North invaded the Three Sisters. The Sistermen responded by bending the knee to the Vale, if they would in return expel the Northmen. Complicating the relationship was that the Sistermen were truly loyal only to themselves, and preferred to be independent. They originally called in the Valemen to expel the Northmen but did not really want to be ruled by them, so this was followed by a rebellion against the Vale backed by the North, followed in turn by a rebellion backed by the Vale, and so on. The Three Sisters subsequently exchanged hands back and forth between the North and the Vale for a thousand years. The fighting finally ended about one thousand years ago, with the Vale retaining control of the Three Sisters.
During the War of Conquest three hundred years ago, the Sistermen seized on the opportunity of the invasion to rebel against their overlords from House Arryn to side with the Targaryens. The rebellion came to an end when a Braavosi fleet hired by House Stark forced the Sistermen to surrender, and the islands briefly came under Northern control. Afterwards they were still administratively considered part of the Vale, now a subdivision of the unified Targaryen realm, but their support of the Targaryens was apparently rewarded with various local privileges, etc.
During Robert's Rebellion, Eddard Stark was on his way to the White Harbor, but was caught in a storm and ended at Three Sisters. Lord Borrel considered delivering him to Aerys, in order to prove his loyalty and to obtain a reward, but his son Godric (the current Lord Borrel) heard impressing news about the victories of Jon Arryn and Robert, and persuaded his father to spare Eddard and send him away.
In the fifth novel, Davos arrives at the Three Sisters on his way to the White Harbor. Lord Godric Borrel treats him properly, according to the guest right. He tells Davos about Ned Stark's visit and the latest news. Although Lord Borrel has a lot to gain by delivering Davos to the Lannisters, he acts as his father did years ago, and allows Davos to leave unharmed.