First things first, you need a good bag to carry and protect your expensive gear. I'm a fan of bags. Anyone who knows me will confirm that bags are my thing. This includes photography bags. I've found that no one bag can cover all of your photographic needs and as such, I have different bags for different situations. The bag I use for carrying lots of gear is the Manfrotto Unica VII Stile Messenger. This bag is great for carrying and protecting your equipment and complies with hand luggage restrictions on most airlines. It's pretty huge (for me anyway; I'm barely 5'1") and so it can take a lot of gear, including a laptop. It has also got a handy pocket at the bottom, which is designed for carrying a small tripod. This will be my hand luggage whilst travelling and will contain all my photography gear, including chargers, along with personal items for the flight.
As I said, however, no one bag will cover all situations, and I find the Unica VII too big to carry on a day to day basis, especially when doing a lot of walking. As such, I will also be taking my Lowepro Passport Sling II. This is a small shoulder bag with a removable padded insert and an expandable section for carrying additional items, such as souvenirs, which you may pick up along the way. I love this bag; it's great for carrying your camera and minimal gear, alongside essential personal items, without being bulky or screaming "rob me, I'm carrying expensive camera gear". It can easily fit my Canon 6D with 24-105mm L lens, an additional small lens such as a 50mm prime, various small accessories (including a Gorillapod SLR Zoom) along with my keys/purse/phone. There is even room to fit a water bottle in one of the outside pockets; essential when walking round in hot weather all day.
If, like me, you are a fan of capturing low light images, you are going to need some sort of camera stabilisation. As I said, despite my best efforts, I struggle to travel light and I take with me two items for this purpose. The first is the Gorillapod SLR Zoom. This is designed to hold heavier SLR camera/lens combinations and is small and light enough to carry at all times. It's also flexible, so it can be wrapped around posts, fences etc to hold your camera. The downside to the Gorillapod is that it requires something to put it on/wrap it round, as it doesn't offer the height of a standard tripod. For this reason, I also use a travel tripod, although I don't carry this round all day, every day and only take it out morning and evening. I use the Hama Traveller Mini Pro, which is not the sturdiest in heavy winds, but the pay off is that its portable and light. I use the ball head from this tripod on the Gorillapod too (see, I can minimise the amount of gear I carry when I set my mind to it!).
It goes without saying that a camera is an essential piece of kit for travel photography and for me, it's my Canon 6D with a 24-105mm L lens. It's not exactly a travel friendly camera, especially for my flimsy wrists, but the image quality is worth carrying it round all day. At some point in the future, however, I'd like to invest in a mirrorless camera, as the quality is meant to rival that of SLR's, but they are much smaller and ideal for travel. I also carry a spare prime lens. It's faster than my zoom and much lighter to carry; nice for taking out on an evening when you don't want so much weight with you. The Canon 40mm pancake lens is ideal.
Until I purchase a smaller camera, a decent strap is needed for spreading the weight of the camera and taking the strain off your neck. Sling straps are great for this, and many have pockets for additional memory cards. Black Rapid make some amazing sling straps, but they come with a hefty price tag and as such, I use a cheap non-branded version. It screws into your tripod socket and the weight of the camera hangs at your hip.
In addition to the items above, I always have an extra battery (fully charged), spare memory cards (try and spread your photo's over different cards, especially if you cannot back up until you return home), a dust blower, lens cloths and a couple of filters (UV, Polariser, ND). And don't forget your battery charger!!!
What are your travel photography essentials?