Famous cuts

Hailed as the greatest cut in movie history, the bone turning to the space satellite/warhead is an example of a match cut.
2001: A Space Odyseey

Equally lauded by filmmakers is this exquisite cut from Lawrence of Arabia.

Apocalypse Now showcasing a huge contrast between war and peace.

A great and perhaps one of the earliest examples of a 'jump cut' in Jean-Luc Godard's Breathless.

A quality example of a process called slow cutting from Clockwork Orange.  Slow cutting is a process which uses shots which last for long durations.