In the near future I'm planning on doing some filming in Costa Rica. I've heard some horror stories of cameras failing in the high humidity, and was wondering what everyone here would suggest to protect my camera and other equipment it?

I had a similar camera (V1U) in Honduras for 2 weeks and did not have a problem.
I've had worse problems in North Carolina going from air condition to outside...which is a really bad idea.

In Honduras there was no Air Condition so the camera was the same temperature all the time.

Hope this helps.

So even with the moisture I should be alright filming there? Just as long as I avoid the drastic changes in temperature?

I live in a climate that can be extremely hot and humid. As Jason said the big problem is when you store the camera overnight in a nice air conditioned room and then the next morning, you take that nice cool camera out into the high heat and humidity. Instant condensation. Tapes will practically glue themselves to the video drum and then you are toast. I have managed to get the condensation dried out by putting the camera in a car with the tape transport open. And then turning the heater on full blast in the car. If you keep the camera at ambient tempertures, you shouldn't have much problem. Just avoid a lot of moisture.

Not strictly a humidity solution but...another useful accessory to consider adding to your already heavy kit bag, or place in the back of the car, is a plug-in travel hair dryer.
That can often get you out of trouble where condensation/damp/moisture is a risk.
For a few dollars at a local store it's virtually a throw-away item - and it could save you a costly repair bill.

If you can't warm the camera up before you go out, a zip-lok bag and 15 minute warmup period is hard to beat. Place the cam in the bag while still in the AC or cooler environment, and it'll warm up without condensing moisture during your drive/walk or wait. You can also turn the camera on in the bag to speed up warmup.

I've had no issues in high humidity weather here in FL. Only time I ever had the problem was several years ago coming out of an ice cold cruise ship into the Bahamas humid heat... instant errror message and 1 hour wait.

Once burnt... once learnt. Zip-lok bag now in every camera bag/case.

Jamie