They are most definitely friends, but they have different feelings towards each other. Although Kairi wants him to return in the second game, she knows that Riku can take care of himself. Riku, on the other hand, worried for her so much in the first game that he went and sacrificed himself to the darkness to get her back. That might just be in his nature though. In any case, it's certain that they remain to be close friends. In the second game, Riku allows her take off his hood to reveal his secret that he has taken on the appearance of Ansem. Later on, she stops him from leaving, and tells Sora who he really is. Had it not been for her interference, the trio might not have been truly reunited at all.
There's certainly a bit of symbolism behind these two. If we take Kairi to represent the sea, and Riku to represent the land, then Kairi & Riku are actually closer than either are to Sora, the sky. It's kind of ironic how those two are always the ones looking after Sora, but Sora is the sky that watches over them. I guess their shared bond would be that they're both the hero's backup crew. If Sora needs help, they go and aid him as much as they can, just like the scene in Kingdom Hearts II where Kairi uses a Keyblade to fight off Heartless alongside Riku.