The brain is a highly dynamic organ that changes constantly through life. During adulthood, there is a general decline in the number of cells. Memory formation is generally thought to be regulated through synaptic connections rather than at the whole-neuron level.
First of all, aging results in a steady decline of the number of nerve cells, so the 'architecture' of the brain changes dramatically regardless its function.
Secondly, memories and other dynamic processes in the brain are typically controlled by altering synaptic connectivity and not so much at the level of the whole-neuron.
Thirdly, neuronal regeneration is confined to but a few areas in the brain, for example the hippocampus where it may, or may not be directly involved in memory formation.
But yes, the brain does dynamically control the synaptic connectivity and notably the synaptic strength of synapses. As Fizz here correctly states, that is called neuroplasticity. Intensive use of certain synaptic connections may result in synaptic strengthening,for example by long-term potentiation (Lynch, 2004). Reversely, abandoned connections may be downregulated through long-term depression.
A general reference work best suited for your basic question would really be a general Neuroscience text book, such as the following online work:
- Purves et al. (eds). Neuroscience. 2nd ed. Sunderland (MA): Sinauer Associates; 2001.
Or for something more up-to-date, yet not online, the bible of Neuroscience:
- Kandel et al. (eds.). Principles of Neural Science
- Lynch, Physiol Rev (2004); 84(1): 87-136