The catalyst for the Civil War in the comic books is a botched bout of superheroics by a young team called the New Warriors. A relatively untrained and unknown bunch of novice, teenage metahumans, the group are more interested in getting some good footage for the reality TV crew that's following them around than actually saving the day. Which is unfortunate because in attempting to ambush some villains in their hideout the situation gets out of hand, one of said bad guys detonates himself, and over 600 civilians die - sixty of whom are children. Woops. It causes a sea change in how the world at large views superheroes. Far from being the benevolent force for good they were always assumed to be, the general public starts to worry that having a bunch of unregulated superpowers running around actually puts them in mortal danger. So the government starts an initiative to have all heroes and villains disclose their identities to them, to register an become legit law enforcement. Something which many heroes aren't happy with, but which doesn't seem like it'd be as big a problem in the MCU, since most of them don't actually have secret identities.
Tom Baker is the Comics Editor at WhatCulture! He's heard all the Doctor Who jokes, but not many about Randall and Hopkirk. He also blogs at http://communibearsilostate.wordpress.com/