There are so few that embody everything that matters in cinema, and he is one of maybe 5. And probably the most important of all.

Just something as endlessly talked about as those jump cuts in Breathless. Extraneous, distracting, unbelievably simple. But also absolutely everything. Up until then most cinematic advancements were about making us forget about the camera. Making it weightless in it's movement. Or a perfect witness to a story it wants to tell. Then all of a sudden Godard is NO. Don't forget this is all a fabricated document on a piece of film and that I can do whatever I want to it. And even though I don't like those jump cuts particularly or even Breathless all that much, nothing could be the same after that.

And then he proceeded to take the maximum and most beautiful liberties with this door he'd just opened

Everything

Breathless - 8/10 - A film that had to be made, the more provocative and formally revolutionary New Wave film is a mess, as electric and scattered as amphetamine damage will allow, a defiant crack in the mirror of cinematic myth.

A Woman Is a Woman - 8/10 - Applying the meta-ironic lens to the musical genre, and the introduction of Anna Karina.

My Life To Live - 8.5/10 - Probably Godard's first film that transcends his formal experimentation into a fully-realized character portrait.

The Little Soldier - 8/10 - Godard's first overt flirting with politics, here the war in Algiers.

The Carabineers - 7/10 - A more simplistic morality tale, and much less visually and stylistically interesting.

Contempt - 9/10 - Godard finally weds his penchant for deconstructing cinematic technique with his deconstructions of human and sexual relationships.  If I didn't know better, I would guess it was at least partly in revenge to Antonioni.

Band Of Outsiders - 7.5/10 - One of Godard's chic-est, and maybe ideal entry-level for hip younger viewers, this outlaw take on Jules and Jim comes off now as one of his most shallow, but still indomitably cool.

A Married Woman - 7/10 - Inferior to Godard's other examinations of bourgeoisie sexuality, no blame to Macha Meril, with a somewhat inexplicable Holocaust allusion running throughout.

Alphaville - 9.5/10 - Also chic, also cool and undeniably artificial, this sci-fi noir simply excels as both a genre exercise and as thoughtful rebellion.

Pierrot le Fou - 9/10 - Like Contempt, this film uses its genre pretenses as little more than an excuse to indulge in cinematic iconoclasm, and is all the better for dispensing such inconveniences as plot for the sake of dissolving the silver-thin screen between reality and illusion.

Masculin Feminin - 8.5/10 - A rich examination of youthful sexual politics, borrowing Truffaut's doppleganger to emphasize this most typically New Wave (sexy, intellectual, naive) of his films.

Two Or Three Things I Know About Her - 9/10 - Godard's superior examination of modern sexual politics and portrait of Woman-Writ-Large. 

Made In USA - 8.5/10 - By this point, Godard was fully embracing surrealism and absurd juxtopositions of intertitle wordplay and non sequitur editing, mixed with an increasingly savage critique of politics, both the vulture consumption of capitalism and the self-negating conformity of Marxism.  And there's something about a murder, yada yada.

La Chinoise - 8.5/10 - Maybe Godard's most infamous film, or would be had anyone seen it, a film that has been frequently confused as Maoist propaganda, as opposed to a satire of the then-emergent fangless radical-chic.  It's prescient enough to pre-date the wonderful scene in Network where the revolutionaries are negotiating their residuals.

Weekend - 10/10 - The culmination of Godard's mid-60s work, where bourgeoisie consumerism, sexual politics and radical literalism become a rapacious monster of modern apocalypse where cannablism becomes the only logical outcome.

One Plus One - 7.5/10 - I'm of two minds on this one.  The first is that I find the in-studio documentary of The Rolling Stones conceiving, arranging and forming their warhorse, "Sympathy For The Devil", to be highly engaging, fascinating and a joy of the magic of witnessing creative inspiration.  The rest of it is a sloggy bore.  Either people feel that this was where Godard began getting really irritatingly pedantic with his politics or that his on-the-nose satire of pedantic revolutionaries was becoming indecipherably insufferable.

Godard's "Dziga Vertov Group" era (1968-1972) is mostly a blind spot as well, and these films are supposedly notorious for where Godard gets his deepest into Brechtian deconstruction and Marxist dogma and the films combine documentary elements with staged scenes of (mostly) political conversations.

One Plus One fits into this group, being half-documentary/half-pedantry, and perhaps it's long been a reason why I haven't ventured further.  The only other film I've seen from this era was Tout Va Bien which is closer to his surrealist era, still an indictment of modernity and consumerism, but it shows more than tells.

The previously mentioned era of his exclusive use of experimental video (74-78) has largely kept me away due to the ugliness of the crude video images.  (I imagine that his interest here was more economic than aesthetic.)

What's called Godard's 'Second Wave' in the 80s is an era that I'm much more familiar with, missing only one film, Keep Your Right Up.  Here, Godard ostensibly returns to something resembling story and character-based films, although his experimental habits manage to shine through.

Every Man For Himself is a domestic drama, the dynamics of exes trying to move on.  Godard's two crime films of this time, First Name: Carmen and Detective, are sexier and more linear but not necessarily so deep.  His pair of spiritual films, Passion and Hail Mary, are more interesting, the latter being especially controversial in its depiction of the religious aspect of the virgin birth and its use of nudity (however mundane).  All of these films, however, would rank at least a solid 8/10, but I'd give the latter two the edge.

King Lear is simply something else, even by Godard's standards.  It's not really about King Lear, for starters, but somehow about all of Western civilization, and Godard (as 'Professor Pluggy') wearing dreadlocks made out of RCA cables is the kind of image that will excite and intrigue, or turn you off completely to the erratic and irreverent approach to the material.  Norman Mailer and Woody Allen appear, only to get immediately annoyed with Godard's antics (a separate half-hour documentary of the Woody Allen scene exists, but I can't find it).  It's close to the perfect Godard film in that it's either everything you'd want from him or everything you'd want to avoid.

Godard's last period has some narrative films, but I haven't really seen those.  Of the ones I have seen, the narrative is subsumed by what are more essentially essays on the nature of film itself, or more generally on art, language, love.  Thematic portraits and audio-visual poems.  In Praise of Love, Notre Musique, Goodbye To Language.  The latter was Godard's first film in 3D, although I saw it in 2D.  All three are fascinating ruminations, and difficult to grasp in one viewing.  But for my money, I think that Godard's greatest late-career (and one of his entire career) accomplishment is his 4 and a half hour documentary Historie(s) Du Cinema, a breathtaking attempt to condense the significance of the entire 20th Century art form through his lifetime's wisdom of montage filmmaking and erudition of stylistic substance.