I think the biggest tip I can give you about safety is to just keep your eyes open.  When you are in Europe act the same as you would in any large American city.   I wouldn’t be too worried, but being a tourist does make you a bit more veunerable than a local (plus getting you stuff stolen can set you back a couple of days).   
 
That being said here are some things I do:
-  I always carry a debit card and a credit card.  When I am traveling with a friend we switch credit cards.  That way if her stuff gets stolen, she has a backup card and if my stuff gets stolen I have a backup card.  When I am traveling alone I keep a hundred dollar bill tucked into my bra just in case .
-  If you have a secure e-mail account then scan copies of your passport, your cards, and any other emergency info you need and send them to yourself (that way you can access it from anywhere)
-  Unlike other travelers I don’t carry my passport in a money belt…  I know some people are going to hate me for saying that.  I just carry a purse that I can fit a waterbottle, my money, my little camera and a couple pages torn from my guide book.  This is a bit harder for guys I find that the best deterant for a pickpocket is someone who doesn’t look like a tourist. 
-  To keep my bag safe on trains and in the hostels I bring along a luggage lock (to lock the main zipper) and a bicycle lock.  Honestly I hardly ever use them.  When I am staying at a sketchy hostel I will lock up my back and attach it to the bedframe (or put it in a locker if the hostel provides that).  On night trians I like to lock my bag to the luggage rack, just because I can sleep a little sounder.  The only time I’ve had anything stolen is when left my backpack open on my bed while I was showering, when I came back someone had stolen my guidebook, whoever they were bypassed the jewlery, the shoes and the clothes, only a backpacker would do that!  (BTW I always take or lock up my passport, cards and camera when I shower) 
-  I wouldn’t worry about bringing a wire mesh bag for your backpack, some people bring these because of a fear that a train theif will slash through the straps of their bag that is locked to the luggage rack.  My point of view is that if a theif wants my dirty laundy and smelly flip-flops that badly they can have them! 
 
I guess my advice is to just keep the important things as safe as possible, have a backup&nbsplan for the worst case senario, and try not to flaunt anything expensive (fancy watches, ipod or fancy camera).  Getting something stolen will only ruin your trip if you let it. 
 
Thats my two cents… I hope that you have a fantastic time on your trip!

That seems like some quality & sound advice. Thanks for the info!

I don’t carry anything of high value in my backpack, at least not where it is easy access.  I use a small single-strap book bag for my dslr camera + carrying case, and I keep an extra debit card and cash in there.  It’s rarely unattached from my body, and i’m pretty keen on someone trying to unzip it from behind.  I keep money, debit card, and passport in my front pocket (perfectly ok if you don’t have big, loose pockets).  If you do have something that you really don’t want to loose, don’t put it in a side pocket, stuff it down under some clothes, make it really hard to find or get out. 
 
By the way, while in transit from US to EU, don’t use luggage locks when it goes on the plane, if security needs to open your bag, they will just cut the lock. 

Wire mesh is worthless, don’t use it. If you’re mainly concerned about the plane flight, it used to be that you were allowed to put your pack in a large plastic bag and twist-tie it shut. May still be able to do so. This is to prevent straps from becoming caught and torn in the airline’s equipment. It does happen. If you can’t go with the bag, make sure to wrap up all the straps as well as you can.