In terms of finding genetic causes of disease, this happens every day, and is practically mundane, but there are two complications towards getting to cures. First, most disease is far far more complicated than a single gene; any single gene may account for just a percent or two of what we call the same disease. Second, knowing which gene is broken does not provide a cure for that disease; even for a given small molecule, determining if it will interact with a gene's protein or have any effect on that protein's structure or function is a task that physics has not been able to tackle. Additionally, the genome has only been available for a mere decade, and for many if not most diseases, the process of going from a known gene target an approved drug is going to take far longer than 10 years.
So the HGP has fueled a huge amount of discovery, is the foundation of nearly all human biology research, and is completely indispensable, but in terms of new cures for various diseases it has not delivered, yet, but really it shouldn't have to.
http://techcrunch.com/2013/04/23/counsyl http://techcrunch.com/2013/04/25/sv-angel-health-informatics
http://www.nytimes.com/2012/07/08/health/in-gene-sequencing-...
This was just one person, sure, but there are a lot of smart people working very hard on making this scale.
Sequencing technology has gotten to a point where it's just blown Moore's Law absolutely out of the water and we can't throw more compute at the analysis problem, we have to make it smarter. The reference genome is used in how that's been made smarter.
It helps to discuss a little bit about how the HGP reference was produced, and why producing it took 10 years and three billion dollars.
The HGP process first had a map made, where the genome was broken into lots of smaller segments. The idea was that this reduced your problem space; any segment of DNA produced from a sample from that portion of the genome came from that area. Then that segment was broken into lots and lots of smaller chunks and then read on the sequencing machines in 600-800 base segments. By the time that sequencing technology reached "max level," the state of the art machine could generate 96 of those segments in an hour's time.
Then you'd calculate overlaps and assemble those smaller "reads" back into a sequence of that chunk you chose from the map. Then someone would audit the computer-generated assembly by hand, possibly ordering up more lab work to fill any gaps or resolve areas of crummy data. Repeat for the next chunk from the map.
Now here's how things work, when we need to do any sort of genomic analysis on an individual:
New technology has the ability to sequence human genomes at deep coverage in 11 days[1], and cranks out 6 billion reads 100bp long from places all over the genome. Computationally, this is an absolutely different animal. You can't feasibly try to re-assemble these reads into a human. So, what we do is use string matching algorithms to "map" a 100bp read back to where it most likely came from, using the HGP genome as a reference.[2] Since obviously your DNA does not match the HGP reference base-for-base, and mismatches/insertions+deletions are really where the interesting data is anyway, there's some leeway for mismatches in the mapping.
At that point, by mapping reads back to where they came from, we end up with a data file that represents an individual's genome. You're able to walk across the genome base for base and ask "So, base 347 of Chromosome 7 is a T in the reference, what is the most likely base on Joe's genome at this point given the reads we have that span this base?"
Mapping things to the reference also allows us to attempt to find really interesting stuff that can cause disease, such as structural variations in the genome. These are instances where large segments are removed, duplicated, inverted, or picked up and moved somewhere else relative to where they "should be."
[1] http://www.illumina.com/systems/hiseq_comparison.ilmn
[2] http://bio-bwa.sourceforge.net/ is the tool that's most popular these days.