If you travel during a country's rainy season you can expect to both get wet and also get some wonderful shots, but only if you are willing to be a bit brave. I thought I would share a couple of tips along with a shot I took this week:
1. Bag It - Instead of buying expensive cases and protective covers for your gear (which I promise, you will never actually have with you when a downpour strikes) just stop into a local shop and ask for a grocery bag (hand them a bit of money or buy something if you are in a poor neighborhood and want to reward the shopkeeper for helping you out.) First make a hole in the bottom of the bag that is slightly smaller than your lens and gently push the lens through it so only the filter is exposed. Get your camera in a comfortable position in your hand then cover the rest with bag, making a hole for the viewfinder as your final step.
2. Don't Be Afraid To Get Wet - Now that your camera is protected, get out there and shoot. I promise no matter how wet you get, you will dry off!
3. Experiment With Different Shutter Speeds - Slower shutter speeds will make the rain streak through the frame while faster ones will freeze it and make it look like little dots. Experiment with both approaches every time so you come back home with a variety of shots. You can set you camera into "T" (Time) mode so that you can adjust the shutter speed and the camera will do the rest.
4. Experiment With Different Focal Lengths - Different focal lengths will have different effects on how the rain will look so zoom all the way in and take a few frames then all the way out and shoot a few more. If you have interchangeable lenses go somewhere dry and switch them out so you can see the different effects.
5. If Your Camera Gets Wet, Buy Rice - I already made a post on how to fix a wet camera so follow the link if you missed that one.
Here is a shot I took in a downpour here in Dhaka, Bangladesh this week. The camera settings and technical info is below the image:

River taxi drivers seek shelter under umbrellas in their boats during a monsoon downpour in Dhaka, Bangladesh.
This image was shot on a 50mm 1.2 lens at F2.5. The shutter speed was 1/160 at ISO 100.