There are simply too many to enumerate here, but Bart Ehrman has written a great little book on the subject called
Jesus, Interrupted: Revealing the Hidden Contradictions in the Bible (And Why We Don't Know About Them). He teaches classes on how to read and analyze the New Testament, which is his specialty. The first thing he tells students is that most people read the NT sequentially, which is how one expects it ought to be written. However, he has his students compare all four Gospels side-by-side and match up events and stories in one with those in the other. That's when the inconsistencies and contradictions begin to jump out at you. For example, not all of the four gospels in mention the crucifixion, and those that do give radically different accounts. They don't even agree on what day it happened. I believe John even had two cleansing of the Temple events.
If you read all four Gospels in parallel, you come up with very different stories and some irreconcilable differences. What has emerged, though, is a kind of composite of the Gospels that Ehrman considers yet a
fifth account of the life of Jesus that is just different from the Gospel accounts. That is the popular one that is taught in most churches and that makes it into the popular media. His book is well worth reading for anyone who is seriously interested in a basic critical overview of what is in the NT.