Only twenty years ago most people in the world of neuroscience believed that the connections between the neurons in your brain were fixed by the time you were a teenager (or even younger)
This is a distortion of history, I think. Ideas about neural plasticity were bubbling around well before 1990s. For instance, Merzenich and Kaas did many experiments published in the early 1980s that showed that if you cut a sensory nerve in a monkey, you saw a major reorganization of the representation of that body in the cortex.
It is true that people thought mammalian nervous systems did not generate new neurons until probably the min-1990s. But then, adult neurogenesis was yesterday’s news to people studying neuroethology, who had been hearing about how new neurons were added to the brains of adult songbirds, like canaries, for years before that (Goldman and Nottebohm, 1983).
Invertebrate neurobiologists had been on the trail of synaptic changes associated with learning and memory a decade earlier (Castellucci and Kandel, 1974).
And, if you think about it, in order for learning to occur and memories to be formed, some kind of change had to be happening at the neuronal level. Psychologist Don Hebb was thinking about how such changes at the neural level might occur back in 1949 (reviewed here).
Previously, people argued about whether those changes were presynaptic or postsynaptic, as though there were only two possibilities. I could make a very long list of ways that neurons might change in response to experience now, and that list shows no sign that it’s reached its limit yet. In fact, less than a month ago, Kuba and colleagues showed yet a new way that neurons can change their propensity to fire: by changing the place on the cell where action potentials start.
We did not suddenly discover plasticity two decades ago. I think the surprise has been not that nervous systems can change, but the number of mechanisms by which they can change.
Additional: Also forgot the work of Nobel laureates Hubel and Wiesel, who studied changes in visual cotices of cats reared under different conditions. Many people thought that it's plasticity, but it's really early in development so doesn't really tell us much about adults.
Castellucci VF, & Kandel ER (1974). A Quantal Analysis of the Synaptic Depression Underlying Habituation of the Gill-Withdrawal Reflex in Aplysia Proceedings of the National Academy of Sciences of the United States of America, 71 (12), 5004-5008
Goldman SA, & Nottebohm F (1983). Neuronal production, migration, and differentiation in a vocal control nucleus of the adult female canary brain Proceedings of the National Academy of Sciences of the United States of America 80(8): 2390-2394
Hebb DO. (1949). The organization of behavior. New York: Wiley.
Kuba H, Oichi Y, & Ohmori H (2010). Presynaptic activity regulates Na+ channel distribution at the axon initial segment Nature, 465 (7301), 1075-1078 DOI: 10.1038/nature09087
Merzenich M, & Kaas J. (1982). Reorganization of mammalian somatosensory cortex following peripheral nerve injury Trends in Neurosciences 5: 434-436. DOI: 10.1016/0166-2236(82)90235-1
Canary picture by meophamman on Flickr, used under a Creative Commons license.