If you use common sense, you should have not a problem at all.
Being an Eagle Scout, I assume you are from the USA.
Europe is in many aspects as safe or safer than the USA, I suspect there
are too many movies like *Taken* which portray Europe as dangerous.

I think your most important problem will be money. Life is relatively
expensive in Europe, so for lodging use hostels or couchsurfing and for
traveling I recommend Interrail (which allows to use rail for a reduced
price in Europe, google it). Public transport is excellent, I think
you never have a problem to find your way.

Crime is in general a bit different in Europe. There are some zones you
should avoid but that should not be a problem by informing yourself
beforehand and/or asking locals.
Mugging is extremely rare and only happens in secluded areas (then it
could happen in daylight) or at night. Muggers almost never use guns,
but either start a blitz attack (pepper spray or hitting ambush) or
corner you using their majority or knives. 

Thieves are another section. In contrast to the USA pickpockets here
could be *really,really* good, so watch yourself. Unfortunately some
pickpockets are children to avoid being punished for their actions.

The most problematic crime here IMO  are rackets: In every major city
in Europe you can see Three-card Monte or shell games which you should
avoid like a pest (Even if you do not play, they are often working with
pickpockets). In the Wikipedia [there is an entire section of scam and
confidence tricks][1] which you should read. Americans are often too
accustomed to politeness and scammers use this to their advantage by
being extremely rude (Going into your vicinity without asking, touching
you, aggressively pledging that you are obliged to pay money, whatever).
Act like a local (using language) who knows that they are scams.
You need to keep your distance, stonewall them or if they are getting really
obnoxious, tell them to *Expletive* off (really).


  [1]: http://en.wikipedia.org/wiki/List_of_confidence_tricks