Vanilla Sky is really underrated in this regard. In starting as a typical romance movie, it is able to more seamlessly introduce the more surreal elements by slowly blurring the line between reality and fantasy. The viewer may first have suspicions and then ignore it, only for it to creep up on them at all once. It sort of comes and goes in waves like an LSD trip.
If you haven't seen it already, the original Spanish version (Abre Los Ojos, 1997) adds an additional melodramatic element towards the beginning. The dislocated feeling towards the end is especially amplified as a result. I highly recommend it.