Your genome is like your genetic 'fingerprint' - everyone's is individual. But it's not really that simple.
Each of your cells contains hundreds of mitochondria that produce energy needed to power it. These started off about 4 billion years ago as free-living bacteria that got eaten but not digested by one of our single-celled ancestors. They have their own DNA - and thus their very own genome. (although some of these genes have jumped over to the nuclear chromosomes). This genome is also technically "yours" ... in this case it is passed down solely along the maternal lineage as sperm don't donate the father's miochondria to the fertilized egg. All of us have "Eve's" mitochondria that's been slowly mutating down the aeons.
In some cells of your body, the genome has been mixed around- some bits deleted, rearranged. The white blood lymphocytes that make antibodies (B cells) do this as they mature in your bone marrow. In this way, your body can manufacture zillions of different types of antibody than otherwise would be possible. The genome in one of your B cells is probably different to the genome in your liver or skin.
Here's where it gets more interesting: When you were a fetus, some of your stem cells managed to get into your mother's circulation- and vice versa. It's now been shown that these can survive at least 38 years! It's also theoretically possible that some of these cells could find their way into the circulation of your younger siblings. If you're a woman, it's even possible that your body contains your mother's genome, your grandmother's genome etc etc. - along with those of all your children.
This situation is known as micro-chimerism.. where there exists a relatively tiny amount of non-self DNA. It may explain some auto-immune disorders. I wonder if children born of 3 parents (sperm, egg, surrogate mother) will be shown to have any immunological differences given the (usual) complete genomic dissimilarity between the surrogate mother and the offspring. Who knows- maybe it might trigger autoimmune disease in the surrogate.
Pediatric dermatologists are often confronted by children born with unusual variations in their skin. Sometimes, there can be too much pigment or not enough, too many blood vessels or too few, too many hairs or too few. There are even conditions that cause acne in certain areas but not others.
The patterning of these changes is often described as streaky, whorled or marbled. It is presumed that they follow the lines of embryonic skin development ("Blashko's lines) and are thus termed "Blashkoid". The idea is that there is an error in cell division in one of the fetus' skin stem cells leading to two genomically distinct populations.
My feeling is that this probably happens all the time - but that most genetic changes are 'invisible' to dermatologists. It's only when the color changes that the condition becomes noticeable.
But- (this is REALLY COOL) it is also possible for 2 non-identical twin embryos to fuse together to form a single individual made of two distinct genomes. (A tetragametic chimera). Actually this sort of thing happens in marmoset monkeys all the time (see video below).
When a male & female embryo fuse, the results can be obvious at birth with a form of true hermaphroditism- both ova and testes present.
When 2 twin sister embryos fuse - or 2 twin brothers- you might never know- perhaps it happened to you. Your skin might show subtle whorls of differential pigmentation.
If you're a woman having fertility treatment and they put 2 embryo's in but only 1 comes out.... maybe you should check they haven't fused!
There are 2 situations where you might find out by accident: custody battles and organ transplant workups.
There has even been a case of fusion on an unfertilized ova, with an embryo forming a chimera of a child and (half) his own mother! (a trigametic chimera)