If you divide the photo into thirds, place objects where the thirds cross.  Align horizons and edges to join the third lines.

Disappearing Lines into Corners: If there are strong lines in the scene, try to get them to disappear into the corner.

Apparently, they eye enjoys following "S" curves.  This rules seems to apply mostly to water, roads and the silhouettes of people.

Monotonous Content:

Some images would make killer jigsaw puzzles - they contain many examples of the same object but with deep detail allows the brain to dwell on and discover arbitrary parts of the photo.

Left right symmetry is the rule in this world - many things have symmetry.  If you can find examples where there is symmetry (where it isn't expect) or symmetry is missing when it should be there, your eye will dwell to reconcile  the situation.

Movement into the Majority of the Frame