Many of my suggestions apply to rainforest conditions; in the Galápagos Islands or the west coast of South America, for example, you will usually be in desert conditions.
I've been to the Galápagos three times, and have written a page of advice particularly aimed at the problems faced there. See: Galápagos Photo Advice.
I use Nikon equipment, so all my specific references will be to that, but most of the major manufacturers have very similar equipment offerings.
I like to shoot wildlife (especially birds), so most of the comments are tailored to that.
If all my Nikon equipment magically turned into comparable Canon equipment overnight, I would still be as happy as a clam (except that it would probably take weeks to learn to use the "backwards" Canon bayonet lens mount). I would be less happy if it turned to Minolta, Pentax, or Olympus, however.
Finally, for a total amateur, I probably spend too much on equipment. If you price some of my equipment recommendations, this will become glaringly obvious.
You can see some of my photos if you start from my home page.
Carry a few "camera condoms". These are heavy plastic bags (I use trash-compacter bags) that you can put your camera inside when it suddenly starts pouring rain. They are made of 3 mil plastic, so they're tough, and can take a lot of abuse before the camera wears a hole in them. Take two or three. They're also handy on boat rides where there's a lot of spray or waves. Put your camera stuff inside for the wet parts of the ride.
Sometimes it gets very hot. Don't cook your film. If you leave it in a black pack on the dashboard of your car in direct sunlight, you'll learn some interesting things about film chemistry. I usually carry 4 or 5 rolls with me, and keep the rest in the middle of my duffle bag so that it's pretty well insulated. If you use professional film that recommends storage in a refrigerator, don't worry too much about a lack of refrigeration for a month or less.
In the rainforest, go on night hikes. Take a flashlight (those head-mounted things make you look like a nerd, but they're great), and look in bushes, under leaves, et cetera. When you get that emerging cicada or huge spider, use the macro techniques (explained below) to get your photos. If there's somebody else with you things are much simpler, since your buddy can shine the flashlight on the subject while you're messing around with your focus, flash, and composition.
Unless you want to give your Spanish a real workout, don't take photos of highly charged political grafitti in Quito in front of a soldier with a submachine gun. Yes, I did it, and found it was a great way to improve my Spanish fluency.
"Skin" your film. Take it out of the cardboard boxes, and if it's not in the transparent film cannisters (like Fuji uses), transfer it to transparent ones. Then put it all in plastic zip-lock bags, and have it hand-inspected so that it won't go though the X-ray machines. That way the inspector can see that it is film, and won't need to open all your cannisters. Putting film through US X-ray machines seems safe, but who knows how much power the machines in Guayaquil use?
I don't like zoom lenses (except for ultra-wide-angle, see below). They're compromises, and I find that I only ever use them at their extremes anyway. If I have a 80-200 mm lens, I shoot at 80 (and it's not short enough) or at 200 (and it's not long enough). A zoom always has more chunks of glass between your subject and your film than a fixed (so called "prime") lens, so it will weigh more and have poorer optics in general. Finally, there are very few situations where you can't back up if you're too close to your subject, so I take the longest telephoto I can, and in the incredibly rare situations where I'm too close, I take a step or two back. This does happen in the Galápagos, but almost nowhere else.
My favorite lens for travelling is the 300mm f/4. I always use it on a tripod -- the Gitzo 226 is a great compromise for travel -- not too flimsy, compact, and solid, for its weight. I use the Arca monoball head, and use the plates from Really Right Stuff.
My second favorite lens is a macro lens. See the section on macro photography below.
I usually take a wider angle lens for people shots. I like them pretty wide (24mm); your taste may be different. A 16mm fisheye in the jungle can make for some pretty interesting shots as well. If I've got extra weight and space, I'll take the 20-35mm f/2.8 zoom. In a cramped boat, you can't always back up, and if you're doing grand landscapes, backing up to make a 35mm work like a 20mm lens might mean you have to back up a half mile. If you're taking photos of people in the jungle, it's often a good idea to use a fill-in flash.
Take too much film. In comparison with what you paid to get to Costa Rica, it's a drop in the bucket. Don't use some new, fancy film that you've never tried before. Use the stuff you're familiar with, or at least shoot and develop a few rolls of the fancy stuff before you go so that you have some idea of the new film's characteristics. Don't even think about purchasing film with only 24 shots per roll.
My life is arranged around two fundamental organizing principles. The most important is, "Park in the shade." The second is, "Never buy a piece of battery-powered gear that doesn't use AA batteries." (Actually, there were only two rules when this page was originally written, but now I have added a third: "When you are on a long bus ride in a third-world country, pee at every opportunity; you never know when the next one will come.") Both apply to photography. Parking is the shade will protect your film, and if everything runs on AA batteries, you just need to bring a big block of AAs on your vacation. It's one of the reasons I chose Nikon -- most Nikon bodies don't use those weirdo lithium cells; they use AA batteries. Same with the big Nikon flashes. Just make sure your flashlight, GPS unit, image-stabilized binoculars, and pacemaker are the same, and life will be good.
It's only fair to state that there's a major religious disagreement on this one, but the answer is: Put a UV filter on the front of any lens you care about for protection. I've become a fundamentalist in this religion after face-planting a $500 macro lens in the mud in Costa Rica with all my weight behind it. I had the UV filter on, and was able to clean up the whole mess in the field with water and patience. I prefer a UV filter to a "skylight" filter for this purpose. A UV filter is neutral for visible light; the skylight filter has a slight pinkish tinge. I figure that if I want pink in my photos, I'll put on the skylight filter. And by the way, unless there's a really good reason, don't stack filters. Take the UV off before you put on the polarizer, for example.
When you buy your UV "protection" filter, get a good one. You paid a gazillion dollars for your lens, right? Why put a piece of crap in front of it? If your lens is multi-coated, why throw it all away with an uncoated filter?
Here's how to shoot hand-held macros with a flash: Set your camera in manual mode (leave on auto-focus if you like), set it at the highest flash sync speed it can handle (for modern Nikons, this is 1/250 second). Make a wild guess at what you can get away with for aperture (you get much better at this with some practice), and set the aperture to that. Take a shot. If the red light on the back of the flash starts blinking, it means you didn't make it -- there wasn't enough light, and you should open up the aperture and try again. If you don't get the blinking, stop it down a bit and try again, until you fail. To get maximum depth of field, you want the smallest opening you can get away with -- you want to be on the hairly edge of what your flash can put out. In other words, you want the aperture to be stopped down so far that one more click will cause the blinking red light. It's sort of like racing bicycles -- if you never fall down, you'll never know how fast you can go. Of course wasting a photo is slightly less painful than sliding down the road at 40 miles per hour with only flimsy bike shorts between you and the asphalt. I use a hefty SB-25 flash; I understand that the SB-24 and SB-26 are similar.
The above instructions, of course, assume that your subject requires a standard exposure. If you need to over-expose (because the subject is very light) or underexpose (because it's dark), just set the exposure compensation dial on your camera appropriately before following the instructions above.
I've used the same techniques with a (non-macro) 300mm lens when the subjects aren't too far away and the ambient light is marginal. With a subject only 15 or 20 feet away, an SB-25 can put out a significant amount of light.
For macro shots, take a flash extension cord so you can hold the flash off the the side. Try shooting from various angles, and try bouncing the flash off white cards, et cetera, to reduce the harshness you sometimes get. My philosophy is that if I get one or two "keepers" off a roll of 36, I'm happy, so if I get a good subject that doesn't run off, I take a lot of shots for insurance.
It got so hot in the middle of the day that eventually it occurred to the woman I was working with that if we loaded our water bottles with ice before leaving, we'd have cool water for most of the day. It seemed like a great idea, so I did so, and stuffed the water bottle in my pack.
The next day, we did catch a butterfly that just didn't seem to be in the guide, so I took out the camera and snapped a few photos. I finished the roll, so I pushed the rewind button, and after a little bit of humming, the motor ground to a halt. It couldn't rewind.
That night, I took the camera back to my room, turned off all the lights, and put it under all my blankets and dirty clothes, reached under the pile, and opened the camera back. Everything was soaking wet inside. The camera, cooled to the freezing point of water, and then exposed to 100% humidity, had caused a huge amount of condensation, both inside and outside the camera. The film was soaked, and stuck to itself, so the rewind motor couldn't budge it.
I pulled out the film (under the blankets), stuffed it in a black plastic film cannister, and sealed the cannister with duct tape. Then I took the camera apart as far as possible and dried it out over a lightbulb. There was no problem with the camera in the future, and a good number of the photos came out fine, too. But I'll never freeze my camera in the tropics again.