No one knows the future, so it's impossible to predict the future of science exactly, but there are a few generalities which seem plausible.
First, science is likely to become more open source. One organization, the Public Library of Science, already publishes six open access online journals, the most popular being PLoS Biology. In the world of science, were subscription to a single journal may cost hundreds of dollars per year, open access has the potential to vastly accelerate the progress of science. The popularity of open access journals and publishing one's papers on websites shows there is immense demand for it to continue.
Science is larger, as developing countries like India and China start graduating tens of thousands of new scientists. This is starting off international collaboration in science like never before, though China needs to do more to collaborate with scientists overseas. More scientists means more research, more ideas, more breakthroughs, more everything. In the same vein, world GDP is expanding, as it has since the Industrial Revolution, making more wealth available to fund science. The world's countries realize that heavy investment in science and technology is necessary for their economies to stay competitive.
Science is becoming simultaneously more interdisciplinary and specialized. As the number of scientists and their median level of knowledge increases, there is more brainpower available to investigate both minutiae and the big picture. These two domains interact, as big picture thinking helps the scientific establishment direct more resources to specializations that matter. By the same token, the establishment is powerful, as it always has been, and can tie up thousands of researchers on dead ends appealing to older scientists who can't let go. Some cursory signs suggest that diversification and tolerance towards dissent is gaining momentum in science, however.
Lastly, the future of science will be about better instruments. Billions upon billions of dollars are invested in building better scientific instruments every year. This includes particle accelerators like the Large Hadron Collider (which cost $5-10 billion USD), space telescopes like the James Webb Space Telescope (to be launched in 2013), any number of new microscopes to probe the nanoscale, and cheap gene sequencing technology to read the genetic code of any animal on Earth.
