The mention of Unicorn was in the King James Bible:
Numbers 23:22 God brought them out of Egypt; he hath as it were the strength of an unicorn.
Numbers 24:8 God brought him forth out of Egypt; he hath as it were the strength of an unicorn: he shall eat up the nations his enemies, and shall break their bones, and pierce them through with his arrows.
Job 39:9 Will the unicorn be willing to serve thee, or abide by thy crib?
Job 39:10 Canst thou bind the unicorn with his band in the furrow? or will he harrow the valleys after thee?
Psalm 29:6 He maketh them also to skip like a calf; Lebanon and Sirion like a young unicorn.
Psalm 92:10 But my horn shalt thou exalt like the horn of an unicorn: I shall be anointed with fresh oil.
In all of these verses, the word once translated "unicorn" has now been translated as "wild ox". (Look up those same verses in the English Standard Verses or NIV (New International Version), and you will see "ox" or "wild ox".
I think it's really a pity that they changed it. Personally, I think it's obvious that some animals in the Bible could have been different animals than what we had today. Is it likely that a "unicorn" actually had wings and one horn as we see it depicted today? I guess it's possible--we don't have any proof either way. But since the word "unicorn" literally means there is "one horn" on this animal, it's likely there was a very strong animal that could have been called a unicorn.
Personally, I think that animals like the Leviathin (that Jose mentioned) could have been dinosaur-like animals. Like all of the dragons and dragons stories could have credibility-cultures all over the earth have stories (what we usually refer to as "folklore" about dragons. It's possible that these animals were the dinosaurs we now discover remains of. The word "dinosaur" wasn't invented until the 1800s anyway, and the skeleton that man found was probably not the first set of bones discovered of such a large animal.
Just my two -cents :)
(PS- that word "unicorn" is still in the King James Version.)
(I may also make a hub about this)