I don't think 2001: A Space Odyssey needs any sort of introduction from me. The movie has been a landmark of cinema since it first released, and is widely considered to be one of the best sci-fi movies ever made. If you haven't seen it at this point, please stop reading this page and give it a watch already!
The technical aspect of 2001 is off the charts. The scope of the cinematography brings out the sheer vastness of space in a way that has rarely been matched. The models of the spaceships and planets hold up to this day, at times looking like Kubrick actually launched himself into space to get a shot. Long shots without dialogue and only featuring silence or the humming of the ship make you truly feel like you're in the endless vacuum with the characters. My favorite portion of the movie has always been the first twenty minutes with the prehistoric man-apes on Earth. Not only are the makeup and costumes extremely effective, but they express so much using only body language and animal sounds. I could watch an entire movie just following the lives of these things.
The storyline of this movie always resonated with me in a very personal way. I'm a guy who places a strong value on transformation, change, and evolution as a person. Big or small, I think you should change fundamental aspects of yourself as you grow and experience new things in life, working to morph yourself into the best possible version of "you" that you can be. This movie follows the transformation of mankind itself by extraterrestrial beings; beginning when men were simply apes, moving into the age of space exploration, and finally evolving into a being beyond human. That's not to say that I literally believe that aliens helped us evolve. But as someone who likes to contemplate what we once were and what we could be, this movie always hits me just right.
This movie may puzzle some people, or be too slow-paced in comparison to modern sci-fi movies. I just urge everyone to give it a chance. Better yet, read the book that was written at the same time. You may find yourself changed afterwards.