Eternal Sunshine of the Spotless Mind
The first time: Joel goes to a doctor to erase the memory of his beloved Clementine, who also had him erased from her memory, in an effort to purge the painful relationship behind forever.
Upon second viewing: Eternal Sunshine is really three stories happening simultaneously: the present day conscious tale of the doctors taking part in Joel’s memory-erasing process, Joel’s actual memories of the relationship as they play themselves out backwards from their present awful state to their first cute meeting on the beach, and the final story of Joel’s attempt to block the doctors memory purge by hiding Clementine in the nether regions of his brain. Most of this becomes clear about 2/3 of the way into the film, but it’s not so obvious the first time, and repeated viewings show just how perfectly each story is woven.

Edward Norton's character from Fight Club is credited as "the narrator." Huh.

Fight Club
The first time: This dude played by Edward Norton becomes pals with a bad influence in the form of Tyler Durden (Brad Pitt) who makes him do very, very bad things.
Upon second viewing: The narrator (Edward Norton) is Tyler Durden, a figment of his imagination and the brains behind all the darkly hilarious and heinous acts performed in the film. Go fight yourself.

It can be easy to forget where Memento is going. And that's the point.

Memento
The first time: Leonard (Guy Pearce) suffers from short-term memory loss causing him to go to great lengths to retain information while simultaneously attempting to solve his wife’s murder.
Upon second viewing: When the film reaches its finale, it begins to feel like a puzzle and it’s up to the viewer to assemble the pieces and draw their own conclusions. It seems clear that Leonard killed his wife… or did he? The film has caused much debate and there is enough evidence to draw multiple conclusions, each with enough supporting evidence to be the absolute one and only correct answer.

The Illusionist tries to trick the audience into believing one thing is true, but closer inspection proves the opposite.

The Illusionist
The first time: Eisenstein is a talented illusionist with a seemingly magical gift who reconnects with his childhood sweetheart Sophie as an adult. Upon realizing he cannot be with her due to things like those pesky European class values and the fact that she is engaged, he has an affair anyway, and her fiancé murders her. Or she simply disappears.
Upon second viewing: Eisenstein and Sophie planned the whole thing and this is revealed upon second viewing with loads of visual cues. Recommended viewing: The Prestige which deals with a similar subject in a story that includes a sick, Twilight Zone-like twist at the end.

This painting from the comic book of the script for Darren Aronofsky's The Fountain illustrates how difficult it was to translate grand concepts of life and death to the screen...

The Fountain
The first time: Bouncing between a trio of characters all played by Hugh Jackman spread across three time periods, each deals with attempting to cheat death in the search for eternal life.
Upon second viewing: The film has a very simple journey played out across each of the three stories resulting in the trio of characters striving for the same goal, but reaching very different conclusions – the acceptance of their own death. It is only the future version of Hugh Jackman who finally gives into the universe and becomes one with the stars reaching a kind of Zen peace. It’s a simple story told in a complex way to force one to think about the larger issues and avoid discussing the issue of experimentation on monkeys.