Here are my favorites:
2 Samuel 24:1
Again the anger of the LORD burned against Israel, and he incited David against them, saying, “Go and take a census of Israel and Judah.” (NIV)
versus
1 Chronicles 21:1
Satan rose up against Israel and incited David to take a census of Israel
The difference in this one is rather subtle
1 Kings 9:23
They were also the chief officials in charge of Solomon’s projects–550 officials supervising the men who did the work.
versus
2 Chronicles 8:10
They were also King Solomon’s chief officials–two hundred and fifty officials supervising the men.
Numerical differences are the hardest to explain away
Genesis 1:25-26
God made the wild animals according to their kinds, the livestock according to their kinds, and all the creatures that move along the ground according to their kinds. And God saw that it was good. Then God said, “Let us make man in our image…”
versus
Genesis 2:18-19
The LORD God said, “It is not good for the man to be alone. I will make a helper suitable for him.” Now the LORD God had formed out of the ground all the beasts of the field and all the birds of the air. He brought them to the man to see what he would name them…
This is a good one when faced with creationists: “Okay, first of all, which creation story are you talking about: The one with the man before or after the animals?”
Matthew 28:19
“Therefore go and make disciples of all nations…”
versus
Matthew 10:5-6
“Do not go among the Gentiles or enter any town of the Samaritans. Go rather to the lost sheep of Israel.”
Matthew 15:26
He answered, “I was sent only to the lost sheep of Israel.” (a few verses later he contemptuously refers to Gentiles as “dogs”)
To many fundamentalists I know, Matthew 28:18-20 is one of Jesus’ most important quotes (especially those groups who are focused on evangelism/recruiting). Nowhere did Jesus ever say to go after the gentiles, so the apostles must’ve no doubt been confused by this… at least until Peter’s vision in Acts 10-11. Some feel these verses were an interpolation to jive with the tacked-on Mark 16:14-20
1 Corinthians 15:5
…and that he appeared to Peter, and then to the Twelve.
This is my favorite. How could Paul “forget” Judas? Of course, this book was written before any of the gospels. I have yet to see a good reason for this “apparent discrepancy”.