The AFI has their list, Filmsite has a bunch as well, there's also the IMDb Top 250, TotalFilm's top 100 and Roger Ebert's Great Movies. Rank and format differences aside, all offer -- in some fashion -- a list of the greatest movies ever made.
Of course, as soon as you start making lists like this, everyone immediately comes out of the woodwork to either question those casting actual judgment (nobody knows the identities of the AFI voters) or their methodology (TotalFilm only considered movies with 5-star reviews) or what the IMDb voters are smoking (The Matrix is 14 places higher than Dr. Strangelove?).
And just what makes a film "great," anyway? Is it as simple as a memorable screenplay? Some powerful performances? A director with singular vision and control? How about a moving soundtrack? Or a compelling story? Rewatchability? Cultural impact? A superintelligent dog? All of the above?
Mankind has waited for the truth long enough. Not only am I going to tell you, once and for all, what the greatest movie of all time is, I'm going to dispense with some of the more well-known pretenders to the throne. This should settle all these arguments once and for all.
And seriously, The Matrix?