Is there any particular area in Brussels to avoid visiting after the recent events?
I am going to visit Bruxelles in a couple of weeks. Mostly museums, restaurants and some nightlife. Is the city centre considered "safe enough"?
UPDATE: A few days after this answer an attack took place. I maintain that attacks are possible, but very unlikely. Just like anywhere in Europe. I added a community wiki answer focusing on the implications for travelers of the 22 March attack. Read that answer if you are looking for practical information.
The last event considered a terrorist attack in Brussels was the shooting at the Jewish Museum on 24 May 2014. Hardly something that would warrant special precautions today.
Most of the terror related news coverage that Brussels recently received has to do with investigations into the November 2015 Paris attacks. Those were planned and executed by people coming from Brussels.
The trigger for your question is probably yesterday's shootout in Vorst. The short story there is that the police wanted to search a suspected empty safehouse. It turned out to be not empty from police point of view and not very safe from terrorist point of view. It resulted in a shootout leaving one suspect dead. This is a rare event, which can happen (but is unlikely to happen) in any city where police is investigating serious crime. That would be any city, I guess.
What does this mean for a visit to Brussels? Not much. You can consider it like any European city for all practical purposes. The security services are on high alert, just like they appear to be about everywhere in Western Europe. If you have already visited Brussels before, you will find that there will be more police officers around and even military (which was unthinkable until a few years ago).
The main safety concern for tourists would be, like in any big city, avoiding to encounter people that will happily carry your wallet for you. All the usual advises that you certainly know hold for Brussels. Some neighborhoods are higher risk than others and pickpockets like crowds and unsuspecting tourists. Nothing new.
Regarding terrorist attacks, Molenbeek is (half jokingly) considered to be the safest region of the city. We suspect that terrorist will not attack their own houses. Regarding other crimes, the story is entirely different, but it is not exactly the most touristy part of Brussels.
Depending on your point of view there might be other "terrorism events" going on in Brussels. At the moment there is an EU summit going on with the leaders of the EU countries (and Turkey for the occasion if I'm not mistaken). In fact it is on the other side of the street from where I am at the moment. Many people would consider those leaders at least dangerous and probably even terrorists. You should not worry about them. We keep them well locked in limo's with bullet proof windows so they can not directly harm you. Indirectly with their decisions, however... If those are the ones you are worried about, you should avoid the European Quarter.
EDIT: you should also be careful about traffic. Some people consider the other users of the road to be terrorists. But I'm not aware about particular recent events. Just the usual crazy stuff going on.
Because of events a few days after the posting of the question, I'm adding a second answer. On 22 March 2016, there were several attacks on Brussels. At the moment confirmed are a bombing of Brussels Airport and an explosion in or near Maalbeek metro station.
The points below are partly speculation, but based on the experience of someone working in Brussels. They might get outdated quickly. I've made the post a community wiki, so feel free to edit.
From the point of view of a traveler:
The main points for tourists traveling to, from and in Brussels:
What if you would like to travel to or from Brussels?
Personally, if it is feasible and you won't lose out financially, I would delay a trip to Brussels for at least a month or so, more for the stress and inconvenience of closed public transit, the fact if you are flying you will have to travel to a distant airport, probably in a neighboring country (Schiphol I would reckon) and take land transportation the rest of the way, and the extra security than any real terrorist threat.
If you were flying in, as I said, your flight will almost definitely be cancelled and your airline will offer a full refund or possibly offer an alternative airport and land transport to Brussels. So you have the opportunity to decide then if you want to cancel your trip. Likewise with hotels, I expect most will be willing to have you cancel your reservation at no cost, even if it is normally not possible, because of the exceptional circumstances. Other costs, well it depends on what you have paid for, you would have to see on a case by case basis. Insurance will be no help whatsoever, the vast majority of policies specifically exclude anything caused by terrorism.
Perhaps consider visiting another European city this time, and save Brussels once things have calmed down a little.
I am the founder of the website CitySafe which aims to assess the crime and safety levels of large cities and countries worldwide (it’s still work-in-progress, but so far I have done c. 40 cities and countries).
For my answer, I am referring to the page about safety in Belgium and Brussels (including a crime map). (FYI, Citysafe’s rating algorithm has assessed a safety level of 70% (100% being the safest) to Belgium, and 60% to Brussels.
Brussels is a safe city for tourists. The main risk is petty crime and pickpocketing in the subway or at the train stations (Bruxelles Midi, Bruxelles North and Bruxelles Central station). There is a high terrorist threat going on in the country; so it is best to avoid very crowded areas and public demonstrations.
The following neighborhoods are best avoided for tourists especially during the night : Anneessens, Anderlecht, Chaarbeek, Brussels North, St-Josse, Marollen and Molenbeek. To view those neighborhoods on a map, check the page: http://www.city-safe.com/europe/belgium/
ISIS has sent about 400 highly skilled terrorists to Western Europe in recent weeks. This means that large scale attacks similar to e.g. the 2008 Mumbai attacks are possible anywhere in mainland Western Europe. Britain is probably safer because it's more difficult to bring explosives and guns into that country. Within mainland Europe, it's relatively easy to transport guns, ammunition and explosives. These are typically obtained in the Balkan region and then transported unnoticed across internal borders to the destination, e.g. Brussels and Paris in case of the recent attacks.
To kill as many people as possible, a terrorist will try to explode his bomb in a confined place where there are many people. So, you can reduce your risk by avoiding such places. Such places with few exits may also be attacked by gunmen who block all exists and start to shoot people. The safest places to visit would be locations in smaller towns or rural areas. So, you could e.g. consider visiting Brugge instead of Brussels. While there you'll also find the same sort of potentially dangerous locations, a terrorist will probably not strike in low profile locations.