Not philosophically boggling, Sliding Doors is a good introduction to the concept of alternate timelines or Many Worlds Interpretation, if you haven’t been exposed to these already.

In Sliding Doors, the timelines intersect in space: the same person is often in the same place in the two alternate timelines. While this may be cinematically delicious, it reeks of fate/destiny and goes against the predictions of chaos theory. For this reason, I recommend watching The Butterfly Effect instead, and some romantic flick other than Serendipity, which also promotes the ideas of fate and life as a deliberate puzzle.