is it conceivable that at some future point in time we will be able to reconstruct organisms based on their genome? If so, would storing your genome result in the potential of being recreated at some future point in time?
In addition to [[C|-|E]]'s remark about epigenetic modifications, there are many more layers of extreme complexity that go far beyond what is encoded in a genome sequence. First, a practical example of the epigenetic stuff: our DNA sequences are made from a four letter chemical alphabet, GCAT. It is very common for the "C" to be chemically modified in a reversible way by the addition of a "methyl" group, which is a carbon atom and three hydrogen atoms. Sometimes this modification seems to be almost random, but sometimes it is critical to the normal function of a cell. The best known example of this is what happens when egg cells and sperm cells are made: they can have the exact same DNA sequences, but their Cs are methylated in very different patterns. In general, you need the combination of methylation from a sperm and an egg to yield a viable embryo. There's an interesting technique where you can take the DNA out of an egg cell or a sperm cell, inject sets of DNA into another egg that has had its DNA removed, and trick the egg into behaving like it's been fertilized. More or less, if you make such an egg using two copies of DNA only from other eggs or two copies of DNA only from sperm, you'll get a screwed up embryo. Make such an egg using a copy of DNA from an egg and a sperm, and you'll get a normal embryo - it's all because of the way that the DNA was previously methylated in the sperm or egg, and it has nothing to do with the actual sequence of the DNA. Later, once a healthy embryo matures and starts making its own sperm or eggs, the methylation pattern is completely reset to whatever is appropriate for the cell type that it is making.
Stuff like that is only scratching the surface. A DNA sequence is a linear sequence, but chromosomes are moving, three dimensional objects that exist in time. They are surrounded by other objects (proteins, RNA, other atoms and molecules) that often stick to them and distort them, and they are floating in a complex goo that can vary in pH, salt content, etc. All of these things need to be in the right orientation and conformation at just the right time and place if you are to have a functioning organism. Complicating things even more, those orientations and conformations need to change, sometimes dramatically, as a cell's environment changes. It's hard to underestimate how rudimentary our understanding of all that is within a single cell, never mind within a whole organism.
It's an imperfect analogy, but maybe you can think of it like this: suppose you print out the source code for Firefox as a book, and then you give it to someone who doesn't know what a computer is and who doesn't have access to electricity. That person would be about as far away from compiling a working version of Firefox as we would be from reconstructing a complex organism with high fidelity from only its genomic sequence. More or less. (That's not to say that it would be impossible to take pieces of DNA from one organism, combine them with components from other organisms, and make some new hybrid. We do that all the time!)
Anyway, we still do not know how to properly read a DNA sequence. You could check the most common mutations causing diseases, but not much more.
...and even then, it's more common for connections between specific mutations and diseases to be correlative, rather than causative. Further, even when a genetic cause of a disease is known with 100% certainty, that does not mean that the disease is even remotely close to being cured.