In ordinary speech anticipate is merely a synonym of expect—“to regard (a future event) as probable”. It is perhaps a little more ‘dignified’ (or pretentious), but not different in meaning.
This meaning, however, is comparatively recent. The nearest definition given in OED 1 (the relevant fascicle was published in 1884) is “9. to look forward to, to look for (an uncertain event) as certain”, which is not quite the same thing.
In formal discourse, consequently, anticipate is at least as if not more likely to bear its original meaning, which was “to take action in expectation of some future event"—in some cases action in order to realize or profit from the expected event, but in its oldest uses, action to prevent or forestall it. Here are some contemporary examples—the first five hits on anticipate in Google Books:
- Blindside: How to Anticipate Forcing Events and Wild Cards in Global Politics, 2008. “Focuses on developing analytical tools to anticipate and manage low-probability events.”
- Anticipate: Knowing What Customers Need Before They Do, 2012. “Staying the course requires a company to anticipate and be ready to decisively address the obstacles that will arise over time.”—
- Anticipate the School You Want: Futurizing K-12 Education, 2008. “Futurizing an academic system requires skillfully honed, practiced and encouraged skills, abilities, and tools for thinking and doing the future. […] a constructed place.”
- Heads Up: How to Anticipate Business Surprises and Seize Opportunities First, 2004. “Provides a four-step approach that business leaders can use to obtain the right information at the right time in an effort to avoid business catastrophes and realize potential opportunities.”
- Proactive Companies: How to Anticipate Market Changes, 2012. “The authors present their new model for Market Proactiveness which shows organizations how to anticipate change and respond to it before they are forced to do so.”