Burroughs-Wheeler transform is not just an academic idea, but is the basis for one of the standard tools for aligning short reads:
http://bowtie-bio.sourceforge.net/index.shtml . There was a mention of compression earlier in the thread, but this is a red herring: BWT also used in bzip2's compression, but the use with DNA sequences is not to compress, but a pre-processing step on the haystack. As epistasis said, when you have billions needles, it makes sense to pre-process the haystack so that the per-needle cost is as low as possible.
As for the FBI's DNA database, this does not consist of sequence data, but, I believe, just microsatellite data. Even if they had full sequence data, it wouldn't make sense to search for new samples against the whole database, but to align the sample with a reference genome and then match the variations across a database of variations.