There are a lot of places to read about the history of molecular biology, but one theme that generally seems to emerge is that discoveries are dependent upon the experimental technology. Take this list of Nobel prizes for molecular biology for instance.
From 1959 until 1969 (and a late ones in 1978 and 1980), you had the functions and structures of important enzymes being elucidated as well as structures of biochemical elements of the cell: polymerases, restriction endonucleases, modifying enzymes of all flavors, etc., and replication and/or structure of nucleic acids and globular proteins. The biochemists ruled, discovering and studying enzymes wherever they could be found.
The high point, I think, was the 1968 prize for physiology or medicine to Robert Holley, Har Gobind Khorana, and Marshall Nirenberg for their work on interpreting the genetic code. Discoveries since then on the central dogma of molecular biology have been what Thomas Kuhn would have called "Normal Science," I would suspect. Reinforcing this perception, the later Nobel prizes for molecular biology, in 1978 and 1980, were for work on restriction endonucleases and the polymerase chain reaction. That is, technologies that opened up the field, not fundamental discoveries regarding the genetic code, etc.
Then, beginning in 1975, you had the cell biologists gaining in recognition and influence, making great strides in revolutionizing their field, when David Baltimore, Renator Dulbecco, and Howard Martin Temin were lauded for their discoveries concerning the interaction between tumour viruses and the genetic material of the cell. But to see more than just this shift from molecular biology to cell biology, you need to take a look at a more comprehensive list of Nobels for medicine.
In that list you see the explosion of cell biology-related Nobels, especially by the late 1980's. 1989-1992, 1994-1996, 1999-2002, 2004, and 2007 were all Nobels in or relating to biology at the level of cells (a few others may arguably be added to this list).
Additionally, new techniques are represented promisingly in the Nobel list, including monoclonal antibodies (1984, medicine), RNA interference (2006, medicine), mouse genetics (2007, medicine), and green fluorescent protein (2008, chemistry).
I don't know what the high point of cell biology will be seen as, but there really seems to be no end in sight. Cells are just at the basis of medicine, being at a critical length-scale for biomedical research. For molecular biology though, it seems that the most important theoretical discoveries have been made, leaving only technological leaps to be added on.
Agree? Disagree? What do you think?