What can you tell about a person, having only their whole genome as information?
I've had a little encounter with this question in the past few months so I'm updating here...

The overall answer is 'really a lot about some things, but not as much as you'd like to think about others.'    There is a scientific genome interpretation 'contest' that has been going on for the past few years called CAGI (Critical Assessment of Genome Interpretation).  This is meant to be a cutting edge set of challenges and its worth looking them over.  Last year there was in particular one challenge - answering questions about ten individuals given only a list of traits and their genome sequences.   

It was not so easy it turns out - simply looking up variants and cross referencing them to the literature led to poor predictions.  Glaucoma, asthma, migrane, irritable bowel syndrome, color blindness, lupus, lactose intolerance are examples from a list of 40-odd contest questions.  If you register onto the site you can get some of the results or there is a paper reporting the results, only four labs tried the challenge and the accuracies were sometimes not great, topping off with Rachel Karchin's lab with an AUC of 90%.  Even some of the phenotypes you think are easy are not a simple lookup.  Genetics is not as pre-determined as we think. 

While we are good at inferring our history and geneology on the other hand.  A reasonable example of this is the 23andme analysis.  They have a lot less information about you than a complete genome sequence, but they do seem to make the most of the 0.0001% of the genome that they do have.

They have a nice lookup of some of the hereditary disease data that is available.  "Increased risk of skin cancer" or for Alzheimers are only chances and its never clear how much your actual lifestyle has impact on 44 outcomes, but its there.  

What they also have is your ancestral analysis which is crazy interesting. it shows where your maternal and paternal lineages come from and how strong.  they have a very pretty heatmap of the continents for this.  National Geographic's DB is probably more sophisticated and ancestry.com also does this.  This is pretty cool.

Also included things like curly hair, color of skin eyes and hair.  

Like SimaPro says they are described in OMIM.  OMIM stands for 'online mendelian inheritance in man' and all the straightforward directly inheritable traits we know of are listed there.  its worth taking a look. There are not a lot of known single mutation genetically inheritable conditions.  

If the genome sequence includes methylation, then some other traits which are epigenetic, not genetic but would also be determined from a genome sequence.  Most famous example of this is MEST which will give an indicator of whether you are a doting parent or not.