Up until now, only people from the Uzumaki clan were shown to host the Nine-Tails:
- Mito Uzumaki
- Kushina Uzumaki
- Naruto Uzumaki
were all shown as the Jinchuuriki for the Nine-Tails.
Why can't people from other clans be hosts of the Nine-Tails?
Up until now, only people from the Uzumaki clan were shown to host the Nine-Tails:
were all shown as the Jinchuuriki for the Nine-Tails.
Why can't people from other clans be hosts of the Nine-Tails?
The answer pretty much lies on the skills and abilities of the Uzumaki Clan.
1st: Members of this clan were very knowledgeable in the art of fūinjutsu, and were both respected, and feared worldwide because of their prodigious skill. Fūinjutsu are a type of jutsu that seal objects, living beings, chakra, along with a wide variety of other things within another object. Fūinjutsu can also be used to unseal objects either from within something or someone.
2nd: The Uzumaki Clan lives in Uzushiogakure. The people of Uzushiogakure were noted to have notoriously long lives, so it gained the epithet "The Village of Longevity". The clan's life force was the reason Kushina survived the extraction of her tailed beast, despite additionally just giving birth only moments before, though she was left severely weakened.
These two (as far as I know) are the reasons why they are a chosen to be jinchuriki.
And another thing, if you analyze the situation, as the parent or member of certain clan that possesses a Kyubi, it is more likely for them to give the Kyubi as an inheritance for the next generation (Ex: Kushina to Naruto: given also the fact that they have the required skill to do that)
Sources:
As explained by Motoi in Chapter 493, Jinchuriki are usually chosen among the spouses, siblings or close relatives of the Kage (and not just in Konoha). This reduces the danger of the Jinchuriki betraying the village, and also serves to protect the Kage and display the Kage's power.
Mito and Kushina were primarily chosen because they were the wives of the First and Fourth Hokage respectively. Them belonging to the Uzumaki clan was also a factor in choosing them over others, for reasons well explained by Christian Mark in another answer. Naruto becoming the Jinchuriki was not pre-planned, it was a decision the Fourth Hokage took during the battle against Kyuubi.
The reason only Uzumaki, is because the members of the Uzumaki Clan, such as Kushina, have a stronger life force and a longer lifespan, an example is that Mito Uzumaki survived since Konoha's Creation to the time of the Third Hokage.
It also explains why Kushina didn't die as soon as the Kyuubi was set free, due to this fact, Only Uzumaki were chosen to become the Nine Tails Jinchuuriki.
All Uzumaki have a great amount of Chakra reserves, and Additionally, have a large amount of experience in sealing techniques.
The reason is none of the above.
Mito wasn't chosen to be a host. She sealed the nine tails in herself of her own accord when it was freed from Madara's control. This is the reason that she, an Uzumaki, was the first Jin of the 9 tails.
Kushina was chosen because even among the Uzumaki clan, her chakra was said to be special and unique.
In Naruto's case, Minato chose his son so that he could be a hero, also selfishly, so that he and Kushina could see him when it's needed.
Only one Uzumaki was ever chosen and that was Kushina.
Because it was first put into an Uzumaki and it has been passed on from generation. It was first sealed into Mito Uzumaki, then Kushina Uzumaki, and during the Nine-Tails attack, Minato sealed the yang-half of the Nine-Tails into Naruto while sealing the yin-half in himself.
So right now, Minato and Naruto are both Jinchuriki's of the Nine-Tails and that also means that Minato is the only non-Uzumaki member with the Nine-Tails inside him since his last name is Namikaze.
The Uzumaki Clan are the ONLY clan capable to holding down the Kyuubi No Kitsune because they have the proper techniques to bind the beast. The Uzumaki are best in fuinjutsu so their chakra and techniques are best when it comes to holding him down. Not only that, others would die becoming the Jinchuuriki.