For jungle adventurers who don't want to immerse themselves in swamp water the whole time they are in the Amazon Rainforest, there is Pico da Neblina. Still one of highest areas of precipitation in Brazil, Pico da Neblina is also the highest mountain, with a height of 2994 meters (9822 feet). This deep into the Amazon, there is no tourist infrastructure and booking with a guide or tour company is a necessity. Furthermore, the gradient can get quite severe, so only truly experienced climbers should attempt this.
If Neblina is beyond your experience level, the nearby village of Sao Gabriel da Cachoeira borders both Columbia and Venezuela and is comprised mostly of a indigenous population of Brazilian Indians, providing an opportunity to interact with an ancient, isolated culture in the midst of the Amazon. Be aware though that more civilized access points like Manaus are a good 850 km (525 miles) away.
To many, that is the appeal, making Nemlina the true epitome of off-the-beaten-path travel!