Bloodline Limits
It is well known that most ninjas have three chakra natures – one primary and two secondary. Some clans produce children that only have the ability to manipulate two natures. This is the price they pay for greater flexibility and power with those two. In these clans, the two chakra natures they have access to merge and blend in unique and unpredictable ways. The special abilities granted by this interaction are known as "Bloodline Limits" or "Kekkei Genkai".
There are two main ways these abilities manifest. The chakra can either be turned outwards, into the world, to manifest as any other ninjutsu technique. These are known as "chakra" type Bloodlines. Alternatively, it can be turned inwards, into the user's own body, granting new physical capabilities. These are known as "body" type Bloodlines.
Bloodline Limits are hypothesised to originate in a mutation, an event which can occur in any human by random chance. One ninja happens to be born with the ability to use these techniques, and he passes it down to his offspring. The interactions of these limits when interbreeding are poorly understood, and most clans with such a Bloodline Limit take every effort to keep the bloodline pure in order to ensure that the limit is passed down.
Theoretically, there are 20 possible Bloodline Limits – 10 combinations of two different natures, each of which can manifest as a chakra or a body type. Only 12 of these – plus the unique Advanced Bloodline Limit of Jinton – are known, however, and it is possible that the mutations to produce the other eight possibilities have simply never occurred.

Chakra types
Futton, or Boil Release: Combining the destruction of fire with water produces clouds of powerful acid.
Hyouton, or Ice Release: Combining water and wind allows the user control over ice and snow. Many powerful techniques are possible with this, including merging the user's body with the reflections in ice. The boundaries between chakra and body type limits are not absolute – there is often crossover, as with this limit.
Jiton, or Magnet Release: A less obvious result, but channelling lightning subtly through the currents of the air allows the user to manipulate magnetic fields to their whim, allowing manipulation of any kind of metallic object.
Mokuton, or Wood Release: The life-giving forces of earth and water combine to allow the user control over plant matter.
Ranton, or Storm Release: This combination of lightning and water natures does not in fact allow the manipulation of weather or storm clouds. Instead, it grants the ability to use bolts of lightning energy which can flow and be guided as easily as water.
Shouton, or Crystal Release: Lightning interacts with earth by altering and fusing it at the molecular level into crystal. This limit allows the creation and manipulation of incredibly strong crystal, and can even put people into stasis with the patience of earth.
Youton, or Lava Release: Combining fire and earth produces exactly the effect one would expect: all-devouring magma.

Body types
Body type limits tend to use less literal interpretations of the elemental natures – though there are exceptions. On the whole, the properties given by each elemental nature can be understood as follows (though note that this is a simplification – the interested student should consult Hyuuga Inochi's treatise On the Properties of Chakra Natures in Body-Type Bloodline Limits, a detailed and extensive analysis of such properties).
Earth: "form" and "patience"
Water: "fluidity" and "control"
Fire: "destruction" and "energy"
Wind: "motion" and "unrestrained"
Lightning: "piercing" and "purity"

Byakugan, or White Eye: The flowing nature of water combines with the piercing vision of lighting to grant perception of the ebb and flow of chakra, and pushes the user's awareness out to encompass the entire world around them.
Mizunokatachi, or Water Form: A more literal interpretation of the nature of water than many body-type limits, users of this limit can transmute their entire body – or any part of it – to water at will. This makes them very hard to injure, as they can simply flow around most attacks and reform after. The most notable user of the modern age is Houzuki Suigetsu of Kirigakure.
Mugentai, or Unlimited Body: The unrestrained nature of wind interacts with the transformational aspects of earth to grant the user control over their own body's individual cells. Users of this limit can merge together to share one body, or even merge with their enemies, altering their cells and proteins from within to cause death. The most notable users of the modern age are Sakon and Ukon of Otogakure.
Sharingan, or Copy Wheel Eye: The most notorious of the Bloodline Limits, the destructive and energy aspects of fire merge with the piercing vision and purity of lightning, to grant a suite of abilities. This is one of the limits that overlap between body and chakra types, as higher levels of the limit grant destructive manifestations of purified fire, among other things. Entire treatises have been written on the Sharingan's abilities and reside in the Konohagakure library; this is not the place for such elaboration.
Shikotsu Myaku, or Dead Bone Pulse: Earth's ability to manipulate form combines with lightning's energy and purity and grants the user complete control over their own skeletal structure. They can grow spurs and protective plates at will, making any surface of their body simultaneously a deadly weapon and an impervious defense.

Other Bloodline Limits
Jinton, or Dust Release deserves a mention here. The only known Bloodline Limit that combines three chakra natures, it merges the earth, wind, and fire natures to disintegrate matter on the molecular level.
The Rin'negan is often considered a Bloodline Limit, but this is erroneous. The Rin'negan is the ultimate transcendence of ninjutsu. It occurs when a ninja manages to combine and reconcile all five chakra natures within himself. In the whole of recorded history, only four people have ever achieved this feat.
Nagato of Akatsuki had the Rin'negan as a birthright, a freak mutation that allowed him access to all chakra natures. Attempts to replicate this genetic quirk have thus far been unsuccessful.
The most famous wielder of the Rin'negan is, of course, the almost-mythical Sage of Six Paths. The creator of ninjutsu as we know it today, he held a true understanding of the nature of chakra, and the truth of the sameness of all natures. In his enlightenment, he was granted the Rin'negan, and with it, the ability to use all chakra naturally.
His enlightenment was replicated many centuries later by Uchiha Madara. Upon complete mastery of the Sharingan, Madara beheld the secrets of chakra and the universe; his unparalleled perception granting him the same insights that the Sage had come to through his own insight and wisdom.
The fourth user of the Rin'negan is known only as Tobi. Virtually nothing is known of his true identity, nor of how he came by the most powerful of the Doujutsu.