Certainly one of the most important events was the discovery of the DNA Double-helix in 1953.
DNA Sequencing sprung to life in 1972, when Frederick Sanger at the University of Cambridge, in England began work on the genome sequence using a variation of the recombinant DNA method. The full DNA sequence of a viral genome was completed by Sanger in 1977. However, Sanger's technique of DNA sequencing was inefficient and no serious work beyond this attempt was even considered, due to the vast resources needed to compute a single genome. At the same time, Maxam and Gilbert publish their own "DNA sequencing by chemical degradation" which became an important method of sequencing for many years thereafter.
During the bulk of the 80's little work was done on furthering the science of sequential analysis, but by 1992, most of the computer technology and lab equipment was in place to allow large companies to sequence up to 100,000 base pair DNA strands - but the cost was very high for any sequencing. While progress was not at a standstill it was clear that no massive work could be done without tremendous effort.
The Human Genome Project began in the late 90's as an attempt to sequence what was considered the ultimate achievement, the human genome. Engineers and scientists worldwide gathered to create new methods in the field. Their goals were twofold: to reduce the overall pricetag associated with performing sequencing and to improve the speed and reliability of these techniques.
We now have numerous sites that can sequence to the 100 million base pair and even higher and at a drastically reduced cost over the older methods used in the early 1990's.