An extended prologue, during the story of Charles Carroll, where we actually see him pass on, and John Gates speaking to Andrew Jackson thereafter, who dismisses the story.
The alternate ending, where two kids in the museum inspecting the now-restored Declaration muse about 'an invisible map hidden on the back of the Declaration of Independence' with one of them declaring it to be fake, in front of a bemused Ben Gates, which leads to the unintended Sequel Hook.
There's a quick moment in the first film where one character is seen grabbing a knife. It was never put to use later; the production team was planning on it, but cut that element out (partly for ratings reasons).
The sequel has a scene in which the bad guy stabs Ben's father. It was cut because it crossed the Moral Event Horizon and undermined his Death Equals Redemption moment later. However, there is still a shot in the film in which the actor is acting like he's injured because they didn't re-shoot that scene.