The I Thought I Should Take a Camera Crowd?
If you are just buying a camera because you think you should take one, think again. Does your mobile take pictures? Use that as well - they won't be very good - but you save some money and have one less gadget to carry around.
The Serious Hobbiyst
At the other extreme - the serious amateur photographer probably already has the gear. If that's what you enjoy doing - then take your gear with you. Yes, I know some people will tell you to leave the expensive stuff at home, but really? Isn't this at least part of the reason why you want to travel?
I do suggest that you make some choices - don't take every lens you own! If you are mainly shooting landscapes make sure you have a wide-angle lens, if potraiture is more you thing than a good zoom. Tripods are very bulky, and may not be practical to carry with you for a day's sightseeing. Also many places that allow cameras will forbid tripods (they get in the way). A small gorilla grip style tripod may be useful though. Most importantly - make sure you travel insurance will cover your gear!
The Rest Of Us
The other 90% of us need to remember that a fantastic camera won't necessarily make you a better photographer! If you don't know the basics of good photography - how to frame a photo, how to focus in on details to make for interesting shots, the rules of thirds, avoiding trees or building growing out of people's heads - then it might be a good idea to start off with a basic photography book - there are plenty out there. Its quite possible to take decent photos with an average camera.
Camera models change all the time, but some names come up every time: Canon, Nikon, Sony. Serious photographers will argue the relative merits, for the rest of us - they all work just fine.