A lot of times, there will be an original character who is a love interest for Naruto's brother. This character may be involved in the story because they are intrigued by the brother's connection to the Kyuubi. Also, there might be a young orphan character that Naruto and his brother take under their wing. This character looks up to them and their relationship with the Kyuubi, and their presence adds a new dynamic to the story.
One common type of original character is a rival. This rival could be another ninja who also wants to harness the power of the Kyuubi, either for good or bad reasons. They might challenge Naruto and his brother at every turn. Another could be a healer who is specifically attuned to the Kyuubi's chakra and can help Naruto when he has trouble controlling it. There could also be an old sage - like character who has been around since the time the Kyuubi was first sealed and has secrets to share.