One major event they met in was the Avengers vs X-Men storyline, which is similar to the Civil War idea in that you have two groups of heroes with very different ideas about how best to protect Earth/people.
The series focuses on the return of the Phoenix Force, the cosmic entity of death and rebirth, as it looks for its new host, believed to be the teenage mutant Hope Summers, who will possess all of its power. Cyclops and the other X-Men want to protect her and prepare her as if she's to be the mutant savior, while Captain America and the Avengers want her handed over to them so they can figure out what to do with her and keep the world safe from a potentially deadly fate. Brubaker described the series as "...one of those legendary ideas: What if the Avengers fought the X-Men?". Marvel's editor-in-chief Axel Alonso said "You've got two populations whose motivations are simple and understandable and defensible. That's part of the beauty of this. You're seeing a story that evolves out of 'What would you do?'"
Ultimately, Wolverine has to choose between two sides (hence why he's in the middle of this and some other covers from the series)