In the wake of the terrorist attacks on the World Trade Centre and several other major attacks since, it is essential to be aware of threats of terrorist action while abroad. Western travellers particularly British and Americans are often singled out as targets by terrorist groups and many see tourists as legitimate targets. While worrying about the risk of terrorism should not be enough to ruin your traveling it is sensible to take precautions. Firstly the Foreign & Travel Office make available a list of countries and regions that it does not advise travel to due to security risk to civilians. This list can be accessed through their web page here.
While it is important to remember that the risk of being caught in a terrorist attack is very small, even smaller than the risk of being caught in a natural disaster you can take precautions against it happening to you. Firstly be aware of the situation before you go, contact the local British Embassy or Consulate if you have any doubts about the safety of the country. Also be aware of suspicious behavior much as you would in a London train station. For example always report unattended baggage in airports and train stations to the appropriate security personnel or directly to the police.
The Foreign & Commonwealth Office travel warnings page.
The US Department of State travel warnings page.