ANSWER: We first need to define evolution before delving into the Bible. The theory is the belief that organisms change and adapt (genetically, in behavior, etc.) with the passage of time. As organisms grow more complex, they compete for resources and struggle to adapt to environmental changes. Those living things, according to evolution, which are best able to adapt and sucessfully compete go on to procreate and pass their genetics to another generation (survival of the fittest) while others do not.
This theory, of course, rejects the Bible and the idea that an all-powerful, eternal God is needed to create and sustain the universe. It, instead, replaces him with the inatimate "gods" of time and chance. It is interesting to note that Charles Darwin's original title of his book in support of evolution was called "On the Origin of Species by Means of Natural Selection."
The Bible does not use the word evolution or directly mention its theories. It does, however, bear record of the universe's creation through a Supreme Being. This is not to say a minor amount of evolving could not have occurred since creation (known as microevolution). Changes below the "family" taxonomic level (such as genus or species) could be perfectly compatible with God's word, since it only talks about creating "kinds" (see Genesis 1:21, 24). The Hebrew word translated "kinds" need not be equated with the term "species" commonly used to defend evolution.
You might have, however, a bigger question in mind, such as whether this theory is compatible with the account of creation found in the Bible or whether scientific creationism is at all rational. The overall system of evolution, of "mono-cell to man," is incompatible with the creation account found in Scripture. It involves ignoring and manipulating the text too much to be plausible. Would we interpret any other book so unilaterally when the story of creation is told very matter-of-fact in Genesis chapters 1 and 2?
The apostle Paul gave his close friend and fellow evangelist an interesting warning in the book of 1Timothy. He told him to "guard the doctrine which has been entrusted to you, avoiding profane, empty babblings, and contradictions of false knowledge that is called science" (1Timothy 6:20, HBFV).
Paul's warning centers on avoiding contradictory arguments that claim to represent scientific truth but instead are nothing more than a lie. One reason why Scripture does not directly discuss evolution or things evolving is that it is "false knowledge." Such theories represent the "empty babblings" of humans who deceivingly wish (as Satan wanted, see Isaiah 14:13 - 14) to replace the true God with themselves.
The following books will aid further study into the fascinating subject of evolution and the Bible. We suggest "What is Creation Science?" by Henry Morris and Gary Parker. Another book, "Defeating Darwinism by Opening Minds" by Phillip Johnson, discusses how faulty analogies and the poor logic of evolutionary thinking can be spotted and exposed. Two other books, Josh McDowell's "More than a Carpenter," and "Evolution: A Theory in Crisis" by Michael Denton, are also great resources for further study of this fascinating topic.