Tarkovsky is too important to reduce to a single list, so I'm going to treat just one film in this post, and hopefully others to follow.
Andrei Rublev or The Passion According to Andrei
IMO, Tarkovsky's great masterpiece and the single most important film about an artist's relation to his culture ever made. But which artist named Andrei is the real subject of this film? Both certainly, and their parallels are interesting, but the film transcends even this dialectic. And, I hasten to add, it's not in the slightest bit pendantic, doesn't draw attention to the question "whose Passion?", and certainly comes to no pat conclusions about either its subject or author.
The film feels almost like an actual found artifact from the middle ages. Its structure is very simple: an episodic tale touching upon various conflicts within the artist, or rather artists generally, in some episodes featuring the main character prominently and in others only secondarily. This very basic structure is bookended by a prologue and epilogue. The prologue is a gorgeous metaphor, essentially a gloss of the Icarus myth: a Russian peasant takes flight from an orthodox church wearing a hot air balloon, marveling at a "God's eye" view of the earth that perhaps only he had ever witnessed at that time. Before, of course, the inevitable crash to the ground. The epilogue is a montage of Rublev's greatest frescoes and icons, essentially his representations of the "God's eye" view granted to only the very greatest artists, and presented to us not unlike a revelation, like stone tablets from the mountaintop.
The episodes that comprise the body of the film deal with various aspects of the artist's life, each touching upon a conflict that seems specific but can easily be generalized to speak to the metaphorical universal "artist". But, again, not in pendantic way. Rublev leaving the first monastery to gain greater knowledge, greater experience... and perhaps greater fame. Kirill's jealousy of Rublev's gifts and attempts to undermine him with Theophanes the Greek (think Salieri in "Amadeus"). Rublev's dialog with Theophanes about the purpose of religion, and hence religious art. The very Christian Rublev's fascination with the pagan rituals, their mystery and mysticism, the connection with nature. The impact of war and political intrigue, and Rublev's act of violence in defense of another that gives rise his need to do penance, to renounce his gift, to seek a practical life. And the final, amazing episode featuring young Boris and the making of the bell. Boris' act of crazy faith, and its success, jarring Rublev from his self-imposed artistic exile.
A simple film, perhaps Tarkovsky's most straightforward save "Ivan's Childhood" and his far lesser student films, but one that evokes infinite layers of meaning. As many times as I've seen it, the well has still not run dry, and it continues to reveal its mysteries and insights. Many of its most significant moments are entirely ineffable, beyond the realm of discourse, existing only as wordless poetry. Sometimes beautiful, sometimes horrible, from the chaste to the vulgar, from the sublime heights of artistic achievement to the depths of violence and torture, it's a film that seems to encompass the whole of the universe. One of the greatest works of art of the 20th century.