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 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 fuckExpletive off (really).