I've only recently discovered Tarkovsky and what a revelation it has been! Stalker is definitely among the very few movies that truly moved me in both an artistic way and an intellectual way - I might even add: in a spiritual way.
The visual elements of Stalker are delicately beautiful. Every image is a poem in itself, a self-contained piece of art within the greater sum of the movie as a whole. The slow rythm and the haunting music make up for a very immersive experience. You forget you are watching a movie - you are, instead, living a surprisingly real experience.
Aside from the artistic aspect of Stalker, there is the philosophical/intellectual aspect. The movie asks questions on three main themes: the nature of art, the nature of knowledge, and the nature of life itself. Each one of these themes is personified by one of the three main characters, each character having, in turn, a moment where he expresses this questionning. This is done sometimes as a simple statement, other times as a calm opposition with another character, like a desperate war, against and along side with others, against and along side with oneself. They go into the Zone hoping to find answers. The Zone is, to me, a representation of our innermost self, the "machine room" of our Human existence, a place too few of us manage to reach, and even fewer manage to understand and use.
The ending leaves suspension marks, suggesting many things, maybe explaining some few things, but definitely asking many questions. Many, many questions.
And suggesting a great many things about our Human nature.