Belgium is generally safe -- even the big cities are low-crime areas. However, Belgium has experienced a creeping spread of drug-related crime, and crimes committed by some poorly integrated members of immigrant communities. In Brussels, the Métro has been plagued by muggers, and though increased police presence and video surveillance have brought this under control, it's still better not to venture alone into deserted Métro access corridors after dark; when other people are around, it's generally safe.
Both Brussels and Antwerp have well-defined red-light zones, in which more than a little caution is in order. Don't confuse these places with the Red Light District up the road in Amsterdam, which is a pretty big tourist attraction in its own right, and mostly safe for casual visitors. Brussels's red-light zone in particular is a creepy, low-life zone, and though Antwerp's is not quite so bad it's still not really a place to go for sightseeing. Bruges and Ghent have only minimal facilities of this kind, so this is not a factor there.
Dealing with Discrimination
The election in 2008 of Barack Obama to replace George W. Bush as U.S. president seems likely to change the status of American visitors to "Old Europe" from one of guests who are not entirely respectable in such delicate company, to that of repentant sinners who finally heeded the advice of their moral guardians and improved themselves. How individual Americans feel about this transformation in their standing will be a matter of personal taste.
Meanwhile, both Holland and Belgium are showing an increase in votes for right-wing political parties opposed, to one degree or another, to immigration, or even to the continued presence of immigrant communities. This applies in particular to those migrants "who do not share European values." Rising levels of muggings, break-ins, pickpocketing, bag snatching, auto theft, and other crimes, attributed, rightly or wrongly, to legal and illegal immigrants and to some ethnic minorities, appear to be fueling the trend. This attitude could translate into discrimination against nonwhite visitors, though the majority of Dutch and Belgians would have nothing to do with this.
Antwerp has both an Orthodox Jewish community and a significant minority of people of North African (Arab) origin. Tensions caused by the Israeli/Palestinian conflict have led to some anti-Jewish attacks. Jewish visitors who dress in a way that clearly identifies them as Jewish should be aware of this, even though the chances of being a victim of such an attack are very small.
Note: Listing some of the possible dangers together like this can give a false impression of the threat from crime or discrimination in the Benelux lands. None of these dangers is statistically significant, and by no stretch of the imagination can any Benelux city be described as dangerous. The overwhelming probability is that you will not notice any of these problems, far less encounter one of them. But it can't hurt to be aware of them.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.