Avoid Crowds and Crowded Areas:   This is what concerns me the most. Avoid long lines and places where people congregate in a stationary or semi-stationary manner. For example, avoid long, slow moving lines by having cards like the Paris Museum Pass or the Rome Roma Pass.  These items give VIP, no-wait-in line access to attractions without having to wait in line.

Take the Bus, Not the Metro:   To me, it seems like it would be easier to get off a bus in an emergency situation rather than trying to get out of a metro station, or even worse, between metro stations.

Plan an Escape BEFORE an Emergency:   I always investigate hotel emergency exits upon check-in.  I try to pick restaurants with an alternate way out, just not a single entrance/exit way.

Check in Early and Travel Light:   In Brussels, we saw a terrorist act in the check-in area of the airport.  My advice would be to get into the secure area quickly.  This can be done by checking in the night before and by only using carry-on luggage.  Priority access such as TSA pre-check helps too.

Be Aware:  See an unattended bag?  Get away and say something to a police officer or safety official.  See a demonstration or protest?  Walk away.  

Carry Trip Interruption Insurance:  With the right insurance, you can get out of a country more quickly in case of certain emergency situations.

Choose Destinations Wisely:  There are places in Europe and South America with less chances of a terrorist act occurring.  Consider that when choosing a place to travel.

Always Carry at least a Passport COPY:  Write on it your name, medical conditions, hotel you are staying at, contact info at home. Carry a city map too.

Leave an Itinerary with Someone at Home:  Make sure family or friends can get in touch with you while traveling.

And if There is an Emergency Situation:  Try your best NOT to panic and for God's sake, help your fellow man.