A few reasons:
1.) God exhibits a very troubling personality, especially in the old testament. Examples: Psychological torture of Saul (1 Sam 16:14), executing David and Bath-sheba's baby for the sin of their parents (2 Sam 12:15), mind controlling Pharaoh and forcing him to be stubborn to give Yahweh grounds for bringing the ten plagues (Exodus 7:1-4 and many other places), commanding the Israelites to go into battle and then abandoning them...twice. (Judges chapter 20:18-24)
2.) The Bible's anti-homosexual stance. I've gotten to know a few gay men and women and I've come to realize that homosexuality is not some casual lifestyle choice. The people I've met have all said they've felt attracted to the same sex since puberty. I refuse to believe an all-loving God would condemn a person to a life of loneliness simply because they are born different. I'm especially angered by Romans 1:26, which when read in context appears to suggest that homosexual urges are the result of abandonment by God, "giving [people] over to shameful lusts." It's almost as though God throws up his hands in frustration saying, "Well if you want to be immoral go ahead; you'll turn out gay eventually." An almighty God would thoroughly understand human sexual behavior and I can't imagine such a God inspiring that nonsense.
3.) Contradictions. You could write an entire book on the subject but for me three stand out:
In Matthew 27:10 the author says that the purchase of the Potter's field was in fulfillment of the word of Jeremiah. Yet the quotation is nowhere to be found in Jeremiah. Instead it comes from Zechariah. Many Bibles with references even point out this fact. Apologetic counter-arguments are laughable. ("The prophecy really was spoken by Jeremiah, it was just never written down in the Bible.")
The three synoptic gospels (Matthew, Mark, Luke) all say that Jesus ate the passover meal and then executed the following day. The gospel of John however, says that he died on the "day of preparation for the passover" (John 19:14)
In 1 Samuel 16 David meets Saul and becomes his armor bearer and court musician. Yet in the very next chapter (17) after slaying Goliath, Saul has no idea who David is (1 Sam 17:55-58). When was the first meeting? You can't meet someone for the first time on two separate occasions.