It always amuses me how Percy manages to make friends with everyone and everything along the way. Even the most impossible ones.
In book 1 TLT: Grover is his best friend despite only knowing him for one school year. Defended him from bullies. Then Annabeth halfway through their quest when she never really opened to anyone. He even got her to give life with her dad another chance.
In book 2 SoM: Tyson, also with one school year only. Also defended him from bullies. Clarisse (sort of), when he told her to go back with the fleece because it's her quest. And of course Blackjack.
In book 3 TTC: Bianca, when she asked him if he was still angry at her for joining the hunters Percy showed understanding for her by trying to see it from her perspective. 'Nah, as long as...you're happy.' were his words. Then Bianca opened up to him about what little of her past she could remember. Thalia, when he figured out her fear of heights and respected her by never mentioning it to anyone and coming up with plans that didn't involve heights for the rest of the quest. Zoe, when he learned of her past through dreams and conversations and empathized with her, proving himself to be nothing like Hercules and earning Zoe's 'perhaps not all men' comment. And there's Bessie, the one creature with the power to bring down Olympus, he saved from netting as if he were just a normal seaturtle, and naming him 'Bessie'. That's just a so Percy thing to do by this point.
In book 4 TBoTL: Nico. Searched for the kid for six months, followed him via IM, then sidetracks off their quest to save Nico by bargaining with Geryon (when that didn't work out, killed him), tried to offer Nico a place at camp, gave him the Mythomagic Hades figurine and told him 'it's okay to be a kid once a while', and invited him inside for cake and ice cream on his 15th birthday. Calypso (at least the og version anyway, I have no idea why she suddenly decided to hate Percy in hoo. Blame rick), when he told her the gods' punishment for her was unreasonable and suggested he could visit her. Rachel, when he explained the myth world to her and trusted her and asked her to join their quest as their guide. (Note that here it's actually Annabeth who talked to her about her issues with her parents even though she initially wanted to hate her.) Mrs. O'Leary, a hell hound, mind you, the first kind of monster to give him an open wound, yet he was all 'no one harms my dog' in TLO when he fought off the entire army of Hades.
Somewhere between the above he became friends with everyone at CHB, enough that people look to his command in the Battle of Manhattan. Chiron is a mixture of mentor and friend. If you count acquaintance there's also Eurytion (Geryon's assistant at the ranch) that Percy persuaded to change his ways, the girl of the river beside the ranch whom Percy chose not to use her waters, and basically all sea creatures and horses.
Seriously, someone give this guy a tiara and crown him the Princess of Friendship already.