As long as you dont go to a country that is unstable the only thing you should have to worry about is pickpockets.
That being said always read a bit up on where you go and what you're gonna do.
Always pays to take care when taking a taxi or going on safari's or similar,
there is always the remote chance your driver/guide will try to rob you somewhere remote.
Check out
www.Roughguides.com or
www.Lonelyplanet.com for info on where you want to travel, pretty extensive and updated guides from both.
Goodluck with your trip