Well, I can't say what moves you personally, but for me, there are a few events I believe are particularly compelling. These events make the Odyssey both and exciting read and contain some universal truisms that make it relevant reading today.
On my list are the events that lead to Odysseus being washed up on the shores of Scheria (Book 5). Here he is being tested and his intelligence shines brightly.
In Book 16, Telemachus Athena reveals Odyseuss to Telemachus and the two devise a plan to get rid of the suitors. This scene is both touching, as father and son are reunited, and exciting as the injustice in Odysseus' home and the just ousting of the vile suitors soon follows.
Penelope has a terrific scene in Books 20-23 when she devises the bow competition. In her own way, as she has proven during her relentless embroidery, Penelope too is intelligent and her loyalty is amazing. The revelation here of Odysseus' true identity is joyful for them both.