Heartwarming / Naruto Shippuden: Ultimate Ninja Storm Generations
After the fight against the older Naruto in "The Tale of Jiraiya," Jiraiya once again mentions how Naruto is the crudest, most annoying, stupidest apprentice he's ever had...but he's also the strongest because while he doesn't simply know what it takes to be a true ninja, he has what it takes to be a true ninja.
Later on, when Jiraiya fights against Pain, he gets a line he never got in the manga: "You give up...trying to make me give up!" To recap: it's the line his character Naruto (who he based off of Nagato, who is now Pain) says in the first ever book he wrote, and it's what Naruto himself later tells Pain. Awesome, Heartwarming, and Tearjerker combined into one.
Both the opening and ending of "The Tale of Minato." The endings of "The Tale of Zabuza and Haku" and "The Tale of Itachi" too, but both are also major Tear Jerkers.
Using Part I Hinata's Ultimate Jutsu against Part I Naruto counts. In the standard version, she knocks her opponent into the air, jumps above them, and uses her Sixty-Four Palms to blast them into the ground, and the attack ends with her straddling her opponent. When she does this to Naruto, she realizes their respective positions, blushes, and jumps off like a frightened rabbit. Every time you do that attack, a NaruHina fan somewhere starts Squeeing. Oddly enough, this doesn't happen when she uses this on Part II Naruto.