How important is motivation in determining the virtue/non-virtue of a karmic action? I ask this question because I assumed the importance of motivation being paramount in determining the virtue/non-virtue of karmic action was widely shared among all traditions. Anyway, I'd like to know if this assumption is correct from practitioners of other traditions.

So how important is motivation in determining whether a particular action is virtuous or non-virtuous?

Are there any actions where motivation is not important? Are there any actions where it is the only thing that is important? Something in between?
Intention is indeed the most important element of karma.

From Dhammapada 1:


  On one occasion, Thera Cakkhupala came to pay homage to the Buddha at
  the Jetavana monastery. One night, while pacing up and down in
  meditation, the thera accidentally stepped on some insects. In the
  morning, some bhikkhus visiting the thera found the dead insects. They
  thought ill of the thera and reported the matter to the Buddha. The
  Buddha asked them whether they had seen the thera killing the insects.
  When they answered in the negative, the Buddha said, "Just as you had
  not seen him killing, so also he had not seen those living insects.
  Besides, as the thera had already attained arahatship he could have
  no intention of killing and so was quite innocent." On being asked
  why Cakkhupala was blind although he was an arahat, the Buddha told
  the following story:
  
  Cakkhupala was a physician in one of his past existences. Once, he had
  deliberately made a woman patient blind. That woman had promised him
  to become his slave, together with her children, if her eyes were
  completely cured. Fearing that she and her children would have to
  become slaves, she lied to the physician. She told him that her eyes
  were getting worse when, in fact, they were perfectly cured. The
  physician knew she was deceiving him, so in revenge, he gave her
  another ointment, which made her totally blind. As a result of this
  evil deed the physician lost his eyesight many times in his later
  existences.
  
  Then the Buddha spoke in verse as follows:
  Verse 1: All mental
  phenomena have mind as their forerunner; they have mind as their
  chief; they are mind-made. If one speaks or acts with an evil mind,
  'dukkha' follows him just as the wheel follows the hoofprint of the ox
  that draws the cart.


Also showing the importance of intention is Dhammapada 124:


  At Rajagaha there was once a rich man's daughter who had attained
  Sotapatti Fruition as a young girl. One day, Kukkutamitta, a hunter,
  came into town in a cart to sell venison. Seeing Kukkutamitta the
  hunter, the rich young lady fell in love with him immediately; she
  followed him, married him and lived with him in a small village. As a
  result of that marriage, seven sons were born to them and in course of
  time, all the sons got married. One day, the Buddha surveyed the world
  early in the morning with his supernormal power and found that the
  hunter, his seven sons and their wives were due for attainment of
  Sotapatti Fruition. So, the Buddha went to the place where the hunter
  had set his trap in the forest. He put his footprint close to the trap
  and seated himself under the shade of a bush, not far from the trap.
  
  When the hunter came, he saw no animal in the trap; he saw the
  footprint and surmised that someone must have come before him and let
  cut the animal. So, when he saw the Buddha under the shade of the
  bush, he took him for the man who had freed the animal from his trap
  and flew into a rage. He took out his bow and arrow to shoot at the
  Buddha, but as he drew his bow, he became immobilized and remained
  fixed in that position like a statue. His sons followed and found
  their father; they also saw the Buddha at some distance and thought he
  must be the enemy of their father. All of them took out their bows and
  arrows to shoot at the Buddha, but they also became immobilized and
  remained fixed in their respective postures. When the hunter and his
  sons failed to return, the hunter's wife followed them into the
  forest, with her seven daughters-in-law. Seeing her husband and all
  her sons with their arrows aimed at the Buddha, she raised both her
  hands and shout: "Do not kill my father."
  
  When her husband heard her words, he thought, "This must be my
  father-in-law", and her sons thought, "This must be our grandfather";
  and thoughts of loving-kindness came into them. Then the lady said to
  them, ''Put away your bows and arrows and pay obeisance to my father".
  The Buddha realized that, by this time, the minds of the hunter and
  his son; had softened and so he willed that they should be able to
  move and to put away their bows and arrows. After putting away their
  bows and arrows, they paid obeisance to the Buddha and the Buddha
  expounded the Dhamma to them. In the end, the hunter, his seven sons
  and seven daughters-in-law, all fifteen of them, attained Sotapatti
  Fruition.
  
  Then the Buddha returned to the monastery and told Thera Ananda and
  other bhikkhus about the hunter Kukkutamitta and his family attaining
  Sotapatti Fruition in the early part of the morning. The bhikkhus then
  asked the Buddha, "Venerable Sir, is the wife of the hunter who is a
  sotapanna, also not guilty of taking life, if she has been getting
  things like nets, bows and arrows for her husband when he goes out
  hunting?" To this question the Buddha answered, "Bhikkhus, the
  sotapannas do not kill, they do not wish others to get killed. The
  wife of the hunter was only obeying her husband in getting things for
  him. Just as the hand that has no wound is not affected by poison, so
  also, because she has no intention to do evil she is not doing any
  evil."
  
  Then the Buddha spoke in verse as follows:
  Verse 124: If there is no
  wound on the hand, one may handle poison; poison does not affect one
  who has no wound; there can be no evil for one who has no evil
  intention.