In Kingdom Hearts, Riku is a calm, cool, collected teen who is not afraid to go far beyond his limits. This shows through when he shows no fear in stepping into the dark portal when Destiny Islands was being consumed by darkness, along with his statement "I'm not afraid of the darkness!" Also, he seems to be aware of Sora's romantic feelings toward Kairi and often teases him for liking their friend( maybe for the reason he has feelings for her as well), such as when he challenges Sora to a race, Sora saying that if he wins, he gets to become captain of the raft they're constructing; Riku ups the ante by saying that if he wins, he gets to share a paopu fruit with Kairi.
He also showed a strong competitive streak, along with a bit of jealousy. He shows his competitive side when he challenges Sora, saying that his heart is stronger than Sora's heart. It is not actually said aloud, but thanks to Maleficent, he became increasingly jealous of Sora. It started with him finding out about Sora's new friends, and his thinking that he had been replaced. The jealousy grew when he learned about Sora possessing the Keyblade. The jealousy turned into rage, resulting in the battles against Sora throughout Kingdom Hearts, and his possession by Xehanort's Heartless.
Though his traits were not too favorable in Kingdom Hearts, he becomes more heroic in Chain of Memories. Riku has many realizations. One of these was him realizing that he let his heart become weak. From that moment on, he began to shy away from the darkness in his heart. Through the scores of fights and battles in Castle Oblivion, he makes another big realization: he can't get rid of the darkness in his heart, and decides to use it without turning from the light like before. He matured immensely, and along with leaving his past behind him, he also left a lot of his unfortunate traits.
In Kingdom Hearts II, he shows a great amount of loyalty and care for his friends. To save Sora, he did everything he could to bring Roxas to DiZ to make Sora whole again, going so far as to give up his physical form for that of Xehanort's Heartless. As Sora journeyed on between the worlds, he dropped him some valuable clues, such as the sea-salt ice cream and the picture.
When he finally is found in the World That Never Was, he repeatedly shows regret, telling Sora that "he didn't want to be found," and almost refusing to come back to Destiny Islands because of his wrongdoings.
Ever since he was young, he had been curious with everything that is outside of his world. Over time, his curiosity became obsession and he began to think of his world as a prison surrounded by water. When the Heartless came, he led them to the Keyhole of Destiny Islands in exchange for a trip to another world. This obsession greatly diminishes throughout the year of Sora's slumber, most likely because he had already seen many other worlds that the curiosity disappeared. When he returns to Destiny Islands in Kingdom Hearts II, he still comments it as a small world, but agrees with Sora's remark that it is only a part of one that's much bigger. This marks that Riku has a better view of his home world rather than imagine as a prison.
Another good personality trait he showed was a strong protectiveness over his friends. He never wanted Sora and Kairi to find out about the time he spent in the darkness. He nearly sacrificed himself to protect Sora from Xemnas' attacks, leaving him injured after the final battle.
Though Riku matures significantly over the course of the series, he still seems to retain some of his old Kingdom Hearts self, particularly his sense of humor; he refers to Sora, Donald, and Goofy as "wise guys" when talking to the Emperor, cracks a joke about Donald and Goofy's intelligence at their expense ("Sora never did pick the brightest friends."), and calls Sora a "total sap" when going to confront Xemnas.