Researchers have created a computer simulation of a neocortical column in a rat's brain. The simulation consisted of 10,000 neurons and 30 million connections between the neurons. Neocortical columns are one of the more advanced parts of a mammal's brain and are the basic building blocks of the neocortex. In humans, the neocortex is involved in higher brain functions such as spatial reasoning, conscious thought, and language.
Scientists with the Blue Brain project, a research initiative between Switzerland's Ecole Polytechnique Fédérale de Lausanne and IBM, completed the first phase of the project in November, 2007. They speculated that the simulation could be extended to that of an entire human brain with a decade. Other experts, however, were not as optimistic, pointing out that the increase in scale would be daunting. The human brain contains roughly 5 million times the number of neurons and connections than what was simulated.
You can read a detailed article of the work on MIT's Technology Review website, including some spectacular images of the the simulation.