A passage that is sometimes put forth to demonstrate that the bible is incompatible with science comes from the 30th chapter of Genesis:
Jacob, however, took fresh-cut branches from poplar, almond and plane trees and made white stripes on them by peeling the bark and exposing the white inner wood of the branches. Then he placed the peeled branches in all the watering troughs, so that they would be directly in front of the flocks when they came to drink. When the flocks were in heat and came to drink, they mated in front of the branches. And they bore young that were streaked or speckled or spotted. (Gen 30: 37-39)
Some background: what we have here is a case of two rascals, Laban and his son-in-law Jacob, trying to outsmart one another. Laban wants to buy favor from Jacob's God, whom he fears only through divination. And Jacob wants to become wealthy at Laban's expense. Jacob makes what appears to be a fool's bargain, to claim as his payment for services rendered all unusually colored livestock (and only those) from Laban's flocks. Jacob then "generically engineers" the flocks to breed, preferentially, the animals of a different color by having them breed while gazing at colorful striped branches.
Jacob, I would say, is by far the most colorful (no pun intended) of the patriarchs. To me it is as if God decided to use one of the patriarchs to make special demonstrations of his sovereignty. It is about Jacob that we are given one of the most explicitly Calvinistic statements in scripture, when Paul, in Romans 9, quotes the Old Testament to tell us that God loved Jacob and hated his privileged (first born) brother Esau. Not content to stop there, Paul then tells us that this choice was made before they were born to demonstrate God's sovereign right of election. To drive home the theological point, and to demolish Arminianism, Paul then anticipates the Arminian response (that's not fair!) and answers it.
But to further emphasize sovereign election, it would seem, we have Jacob himself behaving as a poster child for the cause. Esau was the likable, man's-man of the two brothers, while Jacob was the mama's boy who stole his brother's birthright and his father's blessing. Jacob did not come to God Arminian style, carefully weighing the options in his unregenerate heart before making a personal commitment, from his fallen free will, to God—instead God wrestled him and made him "say uncle."
But back to the passage. If the bible explicitly taught that the animals were born spotted or speckled or striped because of the branches, we would have a serious conflict with science. What we know is that either (a) Jacob believed that to be the case or (b) God, in an unrecorded discourse, told Jacob to do it. Now before the advent of modern theories, theologians more or less took this at face value. For example, Calvin wrote:
Moreover, as it respects physical causes, it is well known, that the sight of objects by the female has great effect on the form of the fetus.
OK, that doesn't really cut it in light of the theory of genetics.
The explanation here is quite simple: it is God's sovereign plan in action. Looking back at redemptive history, we see that it was God's plan for Jacob to be a man of wealth. (All redemptive history lead's back to Joseph's multi-colored coat, the garment of the son of a wealthy man!) Whether Jacob believed in his breeding techniques or whether God instructed him to perform it as a sort of rite, like Moses holding up his rod so that the Jewish army would prevail over the Amalakites, we do not know. In either case, God, not invalid theories of breeding, increased Jacob's flock at the expense of Laban's.
Some will argue that it is too easy to invoke a miracle to explain a seeming violation of science. Tough. I don't do it for your benefit, but for my own. God, by definition, is supernatural and can perform supernatural acts. I have no problem with miracles. Does that mean the bible can never be at odds with science because one can always invoke miracles? It does not. If the bible stated that the universe had no beginning, it would be at odds with science. If it stated (apart from figures of speech that we still use today) that the earth was flat or that it was at the center of the universe, it would be at odds with science. If it stated unambiguously that the earth was formed only thousands of years ago, it would be at odds with science. Miracles, however, are not at odds with science because by their very definition they cannot be explained by science.