It's important to know your camera before your trip. Before my trip to South America, I took a photography class at The Creative Arts Workshop in New Haven, CT. I highly recommend taking a class if you are looking to improve your technical skills. I met a few people along the way who planned to figure out how to use their DSLR while traveling, and found themselves relying on the automatic mode, which won't give you as much control as manual. If you can't afford a class, at least read up on shutter speed, ISO, aperture and exposure - and how they interrelate. It will make it easier for you to concentrate on the creative rather than technical side of photography. Here's a quick online tutorial that I love: Understanding Your DSLR
The Golden Hour
The best time to snap photos is when the lighting is softer and warmer in hue. This happens right around sunset. Sunrise is also a great time to take photos because the light is cooler and more diffuse. It can be hard to take photos in the middle of the day when the sun is harsher and you are dealing with shadows.
As Robert Capa famously said, "If your pictures aren't good enough, you're not close enough." This is why I love shooting with a 50mm lens. Your feet make a great zoom. Zooming in with a telephoto lens can be a great strategy for landscapes, but when it comes to people, it's best just to stand a bit closer than you would normally think. This improves the quality and clarity of the photo. When you are closer, the photo can focus in on details that would otherwise be missed.
Get Farther Away
A go to travel picture for me is always the rooftop view of a city. When taking this type of photo, try to think about what the sun is doing. Is it nearing sunset? Am I shooting into direct sunlight and creating a strange sun flare? No matter what, the key to this type of photo is to be far enough away to capture the most interesting features of the city.
Know Where the Sun Is
Photos of people are almost always most flattering when the sun is shining on the subject's face. The same is true when photographing buildings. If you want to catch the glistening of light on the ocean, take the photo when the sun is low enough to reflect off the waves. Here is a trick for taking a great photo when the sun is behind your subject: Use your flash!
Take the Road Less Traveled
Walking through the main square will give you the same picture everyone else has. Avoiding obvious routes and taking the back roads might lead you to some more interesting subjects or perspectives.
Watch the Edges and Corners
Be mindful that your photo might come out more interesting if you capture not only your intended subject, but also something interesting in the background.
It can be easy to get caught up in photographing landscapes and buildings, but it is important to capture the people you are traveling with as well. Include them in photos of scenery so that you remember not only where you went, but who went with you. It doesn't always have to be the traditional front-facing photograph, either. Spice it up with some nontraditional candids.
Create a Story with Sequential Photos
Taking a bunch of photos in a row can help capture the "bigger picture."