Paris takes Helen after being left alone in Menelaus' house. Paris stealing Helen is significant because it causes Menelaus to call upon Greece to get her back. Which begins the war between the Greeks and Trojans.
"If I kill you I will give back your body to your friends and do you do the same for me."
"Madman. There are no convenants between sheep and wolves, nor between you and I."
Menelaus and Paris fight. Paris begins to lose the battle, and Aphrodite comes to saves him. This is significant because had Aphrodite not saved him Menelaus would have killed him and Achilles wouldn't have been killed by Paris.
Achilles refuses to fight after Agamemnon steals his girl. Achilles' refusal to fight almost lost the war for the Greeks completely.
"This idea is bound to work!"
Achilles rejoins the war after Hector slays his dear friend, Patroclus. Without Achilles it looked like the Trojans would win the war, so with him back on the battlefield they had a much better chance of success over the Trojans.
Paris shoots an arrow at Achilles which Apollo guides to hit him in his only vulnerable spot, his heel. Achilles dies.
Odysseus has the idea to leave a single Greek behind, primed with a tale to make the Trojans draw the wooden horse into the city. His idea can be credited as the reason the Greeks won the Trojan war. The unexpected attack made it impossible for the Trojans to win.