A big one for me was the belief that humans have only existed for 6000 years vs all the archeological evidence to the contrary. Same story for evolution.
Another form of CD also occurs when people participate in ritual behavior with a group. For example, you go to the KH and you have some reservations - maybe someone told you is a cult or you're just not very religious. Out of respect and the social pressure to conform, you bow your head during the prayer and say amen. Because your behavior (participation) just conflicted your belief (these people might be cultists) you will subconsciously change your belief (since it's to late to change your behavior) to minimize the dissonance. The simple act of bowing your head during prayer makes you more inclined to believe what comes next. Same goes for the song. (Went do you think it's often stressed that you need to be on time for the song and stay through the closing prayer?)
A similar effect happens when you conform in other ways. The analysis of the sparlock video on YouTube (by user askreality) explains this effect quite effectively, I thought.