Bloodlines are unique traits that have different effects. Including added regeneration, special bloodline jutsu, and various passive effects.
Depending on how powerful they are (how useful they are to strengthening your RPC), bloodlines are assigned a rank - the lowest being D, the highest being S. Most bloodlines have positive effects and negative effects. The amount of both are based on which bloodline rank you managed to get.
Listed below are the Bloodlines, sorted by rank.
There are two ways to get a bloodline: rolling and buying.
Once you reach Genin rank you will have one chance to roll a bloodline for free at the Old Cabin. You may or may not get a bloodline from this roll, and if you do get a bloodline it will be random. There will be a 20% chance of this happening. The old cabin can be found at 12,6. (Middle of the compass rose on the travel map).
If you get a bloodline you don't want, you can remove it by buying an Etched Stone from the Black Market with rep or pop points.
If you don't get a bloodline, or want a different bloodline, you can buy a bloodline-containing item from the Black Market with reputation points or popularity points. Different items will give you different ranks (e.g. a Ritual Dagger will give you an A-rank bloodline). You can never roll the same bloodline twice unless you have gotten all of the possible bloodlines (as long as it was after the update). In that case, the bloodline will be a random bloodline out of those you have gotten the least.
The only exceptions are S-rank bloodlines, which can only be gained by a lucky roll or by winning an event which has an S-rank as a prize.