A lot of people travel with DSLR cameras as they want to ensure they get the best photos whilst away. But they are very bulky and not easy to tuck away in a bag. This means most people end up wearning them round their neck which to me is bascially the equivalent of walking around with a big swinging sign on your neck saying "Mug me, mug me, mug me". If you like to take great photos but not walk around with a "Mug me" sign on your neck check out the Sony Alpha 6000. It takes stunning photos but is much more compact. Whichever camera you get make sure it has wi-fi as it will make it much easier to back up your photos to your phone, tablet or laptop.
The Olympus Tough camera will not take as pretty pictures as the Sony Alpha 6000 HOWEVER it is waterproof, shockproof and can handle temperatures of -10C. In order to be able to connect this to your other devices via wi-fi you need to get a memory card (which you'd want anyway) that enables this, like the one on the far right. The camera has a whole host of other cool features too, such as still being able to take photos while recording a video and sports modes. It's by far the best waterproof durable camera I've found.
Go Pro cameras are the ultimate in action cameras. The quality of photos isn't as good as on either of the cameras above and you can't zoom in but if you want to scuba dive or film/photograph any more active persuits like surfing, cliff-jumping, motorbike rides or paragliding this is the best camera you can get for it. Be sure to buy the right accessories to use for whichever sports you think you'll want to use it for.