Kurama

The is the most powerful of the Tailed Beasts; a single swipe of one of its nine tails can raise tsunamis and flatten mountains. After the demon fox attacked Konohagakure, Minato Namikaze, the Fourth Hokage, sealed it within his newborn son, Naruto Uzumaki, by using the Dead Demon Consuming Seal, sacrificing his own life to do so.

Background
The demon fox is an age-old natural disaster that can appear out of nowhere and goes into areas where human malice collects and festers. Many years ago, when the founder of the Uchiha clan, Madara Uchiha, defected from Konoha, he met with the demon fox and used his Mangekyo Sharingan to control it and used it to battle against Hashirama Senju, the First Hokage, for revenge. The battle was so great, that it tore the earth apart and it created the Valley of the End, but despite controlling the demon fox's power, Madara was defeated.

Many years later, he allegedly used the demon fox again to attack Konoha (although Madara claimed that the demon fox's attack on Konoha had nothing to do with him or the Uchiha, saying it was a "natural occurrence"). During the attack, the demon fox decimated all the ninja that came to repel it, but was defeated by Minato and Gamabunta. After they defeated it, Minato sealed the demon fox within Naruto, which freed it from Madara's control. Ever since then, the demon fox has a special loathing for the Sharingan and those who use it. The demon fox even remarked Sasuke Uchiha's eyes and chakra are more sinister than its own, because his Sharingan reminded it of Madara.

In the Fire Temple filler arc, Naruto, Sakura, Yamato and Sai travel to the Fire Temple to investigate the mysterious robbing of the graves of three legendary ninja. While investigating, they befriend a young monk named Sora. Over the course of the arc, however, it is revealed that Sora was infused with chakra left over from the demon fox's attack, making him a Pseudo-Jinchūriki, capable of generating a demon fox cloak similar to Naruto's.

Personality
The demon fox is a giant beast of almost complete malevolence. It is intelligent, and has a sadistic and sarcastic personality. However, it does have a distinct sense of honor and pride, and possesses a loathing respect for Naruto and Minato. It became rather angry and scornful at Naruto when he rejected its chakra in Part II, though this might have merely been anger over missing an opportunity to partially usurp control over Naruto's mind and body and thus weakening the seal. The demon fox relishes the thought of killing Naruto, but it knows it has to help as long it's sealed within him or it will die.

The demon fox will go to great lengths to preserve its own life, as shown when it forces its chakra into Naruto whenever his life is in danger. However, it will back down if Naruto threatens to harm or kill himself.

Naruto's Training
When Naruto was pushed off a cliff by Jiraiya (who was trying to teach Naruto how to summon toads), Naruto entered his mind and met the demon fox for the first time. Immediately, the demon fox wanted to eat Naruto, but it found it couldn't because of the seal that kept it within its cage. Naruto then, showing great bravery, demanded the demon fox to give him chakra as a form of "rent". The demon fox seemed confused at this request at first, but it became amused with its Jinchūriki's bravery and realized that if Naruto dies, it dies as well. So it did as it was told since Naruto came all this way.

Invasion of Konoha arc
The demon fox kept quiet till the Chunin Exams when Naruto battle Neji Hyuga in the first round. As Naruto's chakra points were blocked, he called upon the demon fox for chakra. Without hesistation, it gave him enough chakra to force open his chakra points and gave Neji a glimsp of itself.

As Naruto battle Gaara and Shukaku, Gamabunta and Naruto did a Combination Transformation technique and they both turned into the likeness of the demon fox itself. As the battle continued, Naruto called upon the demon fox again in order to awaken Gaara. Once again, the demon fox did so without hesistation.

Search for Tsunade arc
As the Sannin, Tsunade, Jiraiya, and Orochimaru battled against each other, Naruto battled Kabuto Yakushi and performed the Rasengan on him. As the Rasengan hit, Kabuto used his healing chakra to mess up Naruto's heart which was supposed to kill him. As Tsunade tried to save him, the demon fox realized its surroundings were getting darker and darker. It didn't take long for it to realize that Naruto was dying which greatly scared the beast. Despite Naruto being saved (by Tsunade or by himself), this became the demon fox's first brush with mortality.

Naruto vs Sasuke
As Naruto battled Sasuke at the Valley of the End, Naruto was nearly killed by Sasuke and his Jinchūriki form wasn't enough to stop the mad Uchiha. As Naruto floated near lifelessly in the water, the demon fox noticed this and told Naruto to be grateful to it as it gave Naruto more power to enter in his one-tailed transformation.

Sasuke and Sai arc
For the most part of Part II, the demon fox stayed quiet, mainly just giving Naruto power to enter Tailed forms throught the Rescue Gaara arc. As Naruto battled Orochimaru, Naruto slipped through the bars of the seal and the demon fox concentrated some of its power into Naruto to make Naruto going into his four-tailed transformation where the demon fox temporarily gained limited control of Naruto's body. With this, the demon fox made Naruto's body wreck havoc on not only Orochimaru, but on every living thing around it, including Sakura. Yamato then used his Tailed Beast-supressing technique, along with the First Hokage's necklace, which was the key for surpressing its power, stabilzed the transformation and forced the demon fox back in its cage.

Later, as Naruto and company ran into Sasuke again, the demon fox urged Naruto to show Sasuke "their" power. It tempted Naruto to remove the seal so their power could be one. As Naruto refused, the demon fox grew angry and mocked Naruto that he couldn't do anything by without it. However, Sasuke interfered and the demon fox commented that Sasuke's chakra was just like the one person who had more cursed chakra than its own: Madara Uchiha. As Sasuke surpressed the demon fox back to its cage, it warned him not to kill Naruto, he will only live to regret it if he did. After that, Naruto shunned the demon fox because of how it was hurting his friends. Needless to say, the demon fox wasn't too happy about this.

Elemental Training
As Naruto trained with Kakashi Hatake in wind element training, the demon fox started to "experiment" with Naruto's shadow clones by sending chakra into a few of them. However before they could do any real damage, Yamato surpressed them.

Fire Temple filler arc
As Naruto battled Sora (who was using the demon fox's chakra), the demon fox started to force Naruto to accept its power. It appeared it was angry that someone other than his Jinchūriki was using his power. However, the demon fox was stopped as Naruto stabbed his leg and threatened the beast to back off. It begrudgingly pulled back, but not before absorbing Sora's demon fox power.

Naruto vs Pain
The demon fox remained inactive for a long time after Naruto shunned it, it did however refuse Fukasaku when he tried to fuse with Naruto. But as Naruto battled Pain in the mostly destroyed Konoha, Naruto was pinned down by Pain and was about to be captured by the Akatsuki Leader. However, Hinata Hyuga arrived and declared her love for Naruto and as Pain nearly killed her, Naruto exploded into his four-tailed transformation and then slipped into his six-tailed form, which allowed the demon fox to take control once more. While in minor control, the demon fox took this time to destory the First Hokage's necklace.

When Naruto was captured by Pain's Chibaku Tensei technique, the demon fox tempted Naruto to destroy everything that causes him pain and give his heart completely to the demon fox, so that it could destroy everything that was causing Naruto pain, thus distorting the seal to the point where his eight-tailed transformation is released. The demon fox then goes on to gain mental dominace over Naruto by having him removing the seal completely, but ultimately failed when the soul of Minato Namikaze appeared in Naruto's subconscious to stop him, saying that if Naruto ever goes into his eight-tailed form, he would appear inside his mind.

Escape Plan
The demon fox, as expected, seems to have a plan for escape. When Naruto first met Sasuke after his defection, the demon fox told Naruto to remove the seal internally so that Naruto would have full access to its chakra. It has also been stated that if the seal is broken, or if Naruto draws too much of it's power, the demon fox would be released. As such, during Part II, the demon fox eagerly offers its power to Naruto when fighting against Orochimaru and during his later encounter with Sasuke. This plan, however, failed as Naruto refused to use the demon fox's power.

During Naruto's element training, the demon fox was forcing its chakra into one of Naruto's shadow clones. Its reason for doing this is unknown, but it apparently has something to do with its plans for escape.

Also, it rejected Fukasaku when he tried to merge with Naruto during his Senjutsu training for reasons unknown (although it can be safely assumed that it did that so Naruto would have no choice, but to only rely on its chakra and increases its chances for escape).

During Naruto's battle with Pain, Hinata was greatly injured after trying to protect Naruto, causing him to slip into his six-tailed transformation. During this transformation, the demon fox destroyed the First Hokage's necklace as it tried to supress the demon fox's chakra. Since Yamato had stated that his suppression technique was dependant on the First Hokage's necklace being on Naruto, it's concievable that there was more to the crystal's destruction than the events of the time of destruction.

Later, when trapped by Chibaku Tensei, it tempted Naruto to destroy all those who cause him pain, by telling him to remove the seal. But this attempt is ultimately foiled at the last moment by the spirit of Minato.

Activity inside Naruto
As the demon fox's host, Naruto has accelerated healing, unrivaled stamina and speed, massive strength, and access to the demon fox's near-limitless chakra. The demon fox's chakra allows Naruto to perform his signature jutsu, Shadow Clone Technique, seemingly without limit. He is even able to summon Gamabunta, a normally Kage-level feat requiring a huge amount of chakra proportionate to the size of the summoned creature.

Naruto typically accesses this prodigious supply of chakra from the demon fox during extreme emotional states or life-threatening situations. When he first accessed it, the demon fox's innate rage took over Naruto's mind, causing him to strike out at whatever was near him at the time. Afterwards, Naruto learned to exercise more control over the chakra, and he can now retain his mental state when drawing upon small amounts of the demon fox's chakra. It is said earlier in Part I that Naruto's chakra had to overlap the demon fox's while still leaving some of his own chakra for himself. Kakashi has a theory that implies that Naruto may have slightly more chakra than the demon fox's. After Jiraiya's training, Naruto learns to summon a small degree of the demon fox's power at will. To do this, Naruto travels into his own subconscious (depicted as a sewer) and demands the demon fox to give him its chakra, which he calls "rent". The demon fox simply complies with him because it is amused by Naruto's bravery, and it knows that it will die if Naruto dies.

Apparently, while within Naruto, the Mangekyo Sharingan can't be used to control the demon fox. However, someone with good control of a normal Sharingan is apparently still able to suppress its chakra (as demonstrated by Sasuke).

The Seal
As Minato sealed the demon fox within Naruto, he split the demon fox's chakra in two halves, sealing the Yin chakra with the Dead Demon Consuming Seal, thus making it inaccessible to Naruto, but sealing the Yang chakra with the Eight Trigrams Sealing Style, allowing Naruto to access it.

Hiruzen Sarutobi and Kakashi Hatake allude that if Naruto loses all control of the demon fox's chakra, the seal will break and the demon fox will be released. Though the seal is unlikely to break on its own, the chances of it happening increase as Naruto draws upon more of the demon fox's chakra. During Naruto's training with Jiraiya, he used Gerotora, the toadkey with the same seal on his belly as on Naruto's, to "twist" the seal a little. As he did that, it inadvertently unleased Naruto's four-tailed transformation. Jiraiya mentioned that the seal is becoming weaker over time. This was evident in Naruto's transformations, which occur much quicker and with greater intensity than they did in the first part of the series, often against his own will. As seen during Naruto's training sessions, even the slightest amount of frustration on Naruto's part allows the demon fox's chakra to leak out of the seal, which will then rapidly progress to his four-tailed form, or onwards.

The seal also has a final safeguard to prevent the demon fox from escaping. Minato made it so that if Naruto ever transforms into his eight-tailed form, Minato will appear in his consciousness in order to prevent the seal from being broken.

Influences
A is a well-known character in Japanese folklore, and the influence behind not only the demon fox, but many other reincarnations in modern Japanese culture. It likes to play tricks and pranks on people, and on occasions, transforms itself into a beautiful woman and seduces men (obviously the inspiration for Sexy Technique). Also, kitsune are known to keep their promises, a trait Naruto has; his ninja way is to "never go back on [his] word". It should also be noted that every time Naruto loses control and is overwhelmed by the demon fox's chakra, he seemingly gains another "tail" of chakra. This stems from the belief that the more tails a kitsune has, the more powerful it is, with nine tails usually being the limit.

It might also be noted that according to Chinese mythology, the last king of the Shang Dynasty was seduced by a beautiful, but malevolent nine-tailed fox spirit, which eventually resulted in his downfall, and this could have been another source of inspiration for the demon fox.

Quotes

 * "GWAHAHAHAHA! Well I suppose I can't kill you, can I? After all, you die, I die. Your courage is most impressive little boy...very well, as a reward for making it this far, I will owe you my chakra!"
 * "You runt...you really are weak! (Laughs) You better be grateful to me...and to your beloved Fourth Hokage, who sealed me inside a twerp like you!"
 * (To Sasuke) "Eyes with such power and chakra more sinister than my own...you're just like Madara Uchiha."
 * "Destroy everything...destroy everything that hurts you...give your heart to me...I will save you from the pain."

Trivia

 * Many fans incorrectly believe the demon fox's name is "Kyuubi", the direct English pronunciation of "Kyūbi". When the demon fox is referred to, it is usually called "Kyūbi", which just stands for "Nine-Tails". This is similar to the belief that Minato Namikaze's name, before being revealed, was "Yondaime", which means "Fourth".
 * The demon fox's eyes were like that of the Sharingan when it was being controlled by Madara.
 * According to the Third Databook, the demon fox is the only one who knows the truth about the Uchiha clan and about Naruto. However, it appears that the demon fox has no intentions of telling what it knows.
 * According to the Third Databook, the demon fox plans to take over Naruto's body, hence why it keeps telling Naruto to remove the seal.