This is an interesting question. It begs the question, what is a scientific "discovery"?
Chaos theory is almost a legitimate "discovery," because until Edward Lorenz tried to repeat a Navier-Stokes simulation with initial conditions he rounded to three decimal places instead of the six the computer stored, people were not totally convinced of such "sensitivity to initial conditions." So that really is a place where the computer simulation really allowed a new phenomenon in the theory to be observed.
Not quite science, but pure math has some "discoveries" that come from computers. Was the Mandelbrot Set "discovered" when it was simulated, or was it discovered when the defining equation was written down? It gets hazy.
Simulations are used all the time in physics to get numerical estimates. For example, a lot of computational power has been devoted to simulating the equations of GR, such as estimating the magnitude of gravitational waves from colliding black holes. But there's really no "discovery" here unless you're very impressed with numerical values. Similar things are often done in quantum theory, e.g. simulations are often done to find variational solutions to many-body wavefunctions, and perturbative QFT calculations involving Feynman diagrams are often calculated on computer. Still not really a "discovery" though.
Then again there are some actual nontrivial hypotheses that people were only able to arrive at using computers. I don't think any good ones have been verified yet but they've been proposed, so that's why I call them hypotheses. For example, astronomers simulated the history of the solar system, and the simulations seem to indicate that both Neptune and Uranus actually originated inside the orbit of Saturn, and subsequently moved into their current position. See here:
http://arxiv.org/abs/astro-ph/0111290. There's even a paper on arXiv which says that similar solar system simulations indicate there was an extra gas giant in our early solar system!
http://arxiv.org/pdf/1109.2949v1.pdf
Other simulations that give nontrivial facts are models of climate-changing ocean flows and how they led to ice ages. I have heard (no reference though) that someone performed a simulation of the oceans over the next few years, incorporating global warming, which led to the prediction that global warming would divert the gulf stream, and then (counterintuitively) as a result of the gulf stream being diverted, the polar ice caps would grow super rapidly sending us into another ice age! I don't know how you could cook that up without a simulation. (Here's a sort of related reference on ocean modeling and climate change http://www.psc.edu/science/OKeefe/OKeefe.html )