In the books, the ropes simply wrap themselves around the centaur's arms and chest; in the film, they also encase his throat, slowly strangling and crushing him while forcing him to the ground. The ropes were animate and therefore could move and constrict their victims similarly to a constrictor snake.
In the film adaption of Harry Potter and the Deathly Hallows: Part 1, a Snatcher is seen casting this spell on Ron Weasley who is bound in chains, of course it could have been a similar spell such as "Incarcereta" (which was used in an early script of the Half Blood Prince film when Harry attacked Snape for killing Dumbledore) but it seems most likely that it was Incarcerous.
Also in the film adaption of Harry Potter and the Deathly Hallows: Part 2, while fighting their way down to the boathouse, Harry is seen casting this spell where a great flash of orange light escapes his wand and a Death Eater that was trying to lunge at him was instantly bound in chains, again it is unclear if this was Incarcerous or a different capturing-type spell.
An etymologically and functionally related spell is Incarcifors, which transforms objects into prisons to restrict a person's movement.
Based on conjecture, it is likely that Relashio or Emancipare could act as counter-spells to Incarcerous. The Revulsion Jinx would be able to release a person from the binding ropes of Incarcerous, while the incantation for Emancipare is derived from Latin for "set free", suggesting its ability to release a person from any form of incarceration.
Based on the text files from the PC version of LEGO Harry Potter: Years 1-4, Incarcerous may have been intended to have a different effect from how it acts in the final game. In the released version of the game, Incarcerous is one of the "joke spells" used only to temporarily incapacitate minifigures. The text files of the game, however, call it "the Indy whip tie" [sic], presumably meaning the spell was originally meant to act similarly to Indiana Jones's whip from the LEGO Indiana Jones games.
↑ 7.07.1Harry Potter and the Goblet of Fire, Chapter 36 (The Parting of the Ways) - "Then he raised his wand once more and ropes flew out of it, ropes that twisted themselves around Barty Crouch, binding him tightly."