Non-European style "unicorns":
* Kirin (Japan) [info]
* Karkadann (Persian/Arabic)

"The unicorn is the only fabulous beast that does not seem to have been conceived out of human fears. In even the earliest references he is fierce yet good, selfless yet solitary, but always mysteriously beautiful. He could be captured only by unfair means, and his single horn was said to neutralize poison." -Marianna Mayer [The Unicorn and the Lake]

"The unicorn, through its intemperance and not knowing how to control itself, for the love it bears to fair maidens forgets its ferocity and wildness; and laying aside all fear it will go up to a seated damsel and go to sleep in her lap, and thus the hunters take it." -Leonardo da Vinci [From notes accompanying, "Young woman seated in a landscape with a unicorn", an early sketch never realized as a painting]

"scarcely smaller than elephants. They have the hair of a buffalo and feet like an elephant's. They have a single large black horn in the middle of the forehead... They have a head like a wild boar's... They spend their time by preference wallowing in mud and slime. They are very ugly brutes to look at. They are not at all such as we describe them when we relate that they let themselves be captured by virgins, but clean contrary to our notions." -Marco Polo [An eye-witness account]

"Will the unicorn be willing to serve thee, or abide by thy crib? Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee? Wilt thou trust him, because his strength is great? or wilt thou leave thy labour to him? Wilt thou believe him, that he will bring home thy seed, and gather it into thy barn? -Job 39:9-12 [The Bible, KJV] (Historical documents record that King James had two unicorns in his menagerie)