Never even crossed my mind to worry when I was in Rome over Christmas. The only day that I saw significant security was the day that Saddam was executed. You have more to worry about from pickpockets and general scammers than you would about terrorism. If they're on a group excursion there would be even less to worry about.
Cash is still king in Europe and any anti-American sentiment that some may feel is quickly bypassed when a transaction could take place. I found even knowing even a little bit of passable language for the region goes a long way. We'd like people to speak English here, why shouldn't they expect the same from us?
The only danger I ran into was how expensive it is...dollar don't go a long way there anymore... :)
Agreed. Petty theft, pickpockets, agressive panhandling and scammers are of greater concern, but as long as you are alert this should be no problem either. (Watch for people with groups of children begging for food/money where the children swarm around you.) Presumably if you are on the tourist route you will visit mostly large cities. If you come from a rural area this may be a bigger difference than being in Europe.
What cities will you visit?
If you visit any countries where the driving is on the left, remember to look for traffic in that direction while crossing the street. To be safe, get in the habit of looking both ways (and in some countries it's inconclusive which side of the road they drive on from observation). This may sound silly, but getting hit by a car because you were looking the 'other' way is a real danger. Also, lots of little vespas and motorcycles which drive down between lanes of traffic, watch for them also while walking through stopped traffic.
Learn a few words of the language. A few please and thankyou words in each language go a long way.
Don't let the cautious travel books and hyped media of doom deter you.