The best time to visit the Amazon basin is during the "dry season." Although there's no true dry season in a rain forest, it rains less during July and August; it rains most in January and February, and it's hotter between February and June. For Amazon cruises out of Iquitos, high water season is best (mid-November-June). Although there's no true peak tourist season, plan well in advance anyway, as some jungle lodges often take in large groups, and cruise boats can be full.
All southern Amazon-basin reserves are best visited between May and October, the driest months; the lodges are open year-round, though rivers may overflow and mosquitoes are voracious during the worst of the rainy season. Tambopata sees a well-defined wet season/dry season; Manu's rainfall is more evenly dispersed throughout the year. During the dry season, especially July, sudden friajes (cold fronts) bring rain and cold weather to Madre de Dios, so be prepared for the worst. Temperatures can drop from 32°C (90°F) to 10°C (50°F) overnight. No matter when you travel, bring a rain jacket or poncho and perhaps rain pants.