She was also looking out for him in Tel'aran'Rhiod to the extent that Ishamael boasted that she would never be strong enough to protect him. She also stood beside him during her Accepted test. She also helped him during the battle against Sammael, despite having thought about the moral implications of using the One Power in battle since her time with the damane. But regardless of these, Min's vision specifically said Rand needed Egwene and the others to win in order for him to win; so their fates are tied together and for much of the series, he hated Aes Sedai due to his mental issues and Egwene was lumped in with them.

I don't really count the scenes involving relationships, considering they are all handled with the maturity of a junior high school student's first zit.