That's a very broad question, but there's plenty of books in the library on travel/ outdoor photography can you can read and they'll give you plenty of pointers on how you can get yourself some memorable images. Seriously, there's a lot of good books in the library that should see more reading than they already have. Off the top of my head, I can't remember too many titles, but some sparse details on sound books:
The AVA Guide to Outdoor Photography by Cathy Joseph
The AVA Guide to Travel Photography by Keith Wilson
Photos With Impact by Tom Mackie
Learning to See Creatively: Design, Color & Composition in Photography by Bryan Peterson
National Geographic Photography Field Guide: Secrets to Making Great Pictures, Second Edition by Peter Burian and Bob Caputo
National Geographic Photography Field Guide: People and Portraits by National Geographic Society
On The Road: The Art Of The Journey: Stunning Images From Reuters by Julie Knight
Usually it requires a deal of effort to get the right shots. It's about getting the right lighting (ie. waking up to photograph early and staying out late), the moment etc. If you start photographing a site when there's plenty of other tourists there, you might be in for a tough time because things will be very cluttered. Also, you'll probably be photographing things which have already been photographed to death. Look for interesting viewpoints. Don't get too carried away with one thing either but keep your eyes open for other things, such as interesting interactions amongst the locals, a flower growing in the corner etc.
The usual common-sense things would apply. Go together with a few others in a group, watch where you step, and always check that your wallet is with you. Don't flaunt your camera in unsafe areas. If you're not sure of the country's customs and the like, read up the Lonely Planet guide to familiarize yourself with it so you don't photograph sensitive stuff. Furthermore this has the benefit of showing you where the interesting locales are so that you can plan your route of advancement.
DSLRs can go through X-rays, no problem (they are unaffected by the rays). Nowadays the x-rays are even supposed to be film friendly and I brought some fast ISO 800 film through in the past with no trouble at all.