Backpacking is safe, as long as you exercise common sense in
looking after your own security, and your belongings. It's good to
at least have a partner on the trip who can at least help to look
after your big backpack while you visit the toilet. 
Seriously, it's good value for money kind of travelling and it's
the only way to really mingle with the locals, get to know how the
average person lives, etc. since package tours will only take you
to the touristy places of interests and shopping malls. However,
lots of planning is needed, and you'll also need a contingency plan
if say, you miss the train, or the domestic flight is cancelled due
to bad weather, etc. (that is, for long trips).