Since they lacked articulate speech, Homo Erectus and Nenderthal weren't able to give instructions or pass down wisdom in the same way as Homo Sapiens with their larger brains and refined language. Again, its clear to see why over just a few tens of thousands of years, the other human species had finished and only one remained; modern humans.
There is strong evidence modern humans may be the result of some hybridisation between Homo Sapiens and Neanderthals. It would explain a lot like the apparent sudden expansion of brain size that modern humans have had in the last 100,000 or so years. There is an explanation however.
Since studying the neanderthal genome, it now seems very apparent that the gene which allows for speech was also present in Neanderthals. Modern humans may have inherited it from them, but Neanderthals lacked the brain capacity to use it effectively. As language become increasingly articulate and social interactions more complex, our brains got bigger.
As for modern ape species, we aren't 'descended' from them. That is a common misconception among creationists. They are simply the descendants of prehistoric ape species. They do have common ancestors with us if you go back far enough, for example, got back around 12 million years and modern humans have a common ancestry with Orang Utans. Go back 200 million years and all mammals have common ancestory with birds and reptiles, go back 500 million years and we have common ancestry with fish. Modern apes and monkeys still thrive (though some species are in danger from human deforestation). They are still around at least for the time being because they weren't competing for the same evolutionary niche as humans. Monkeys stayed in the treetops, while humans had moved out of the forest hundreds of thousands of years ago.
Evolution isn't some whacky idea that everybody likes just because it pisses off Christians, it is solid science based on centuries of study, observation and discovery, un-swayed by dogma, like all science. Few Christians would say the world was still flat, unless they were perhaps crazy. Unfortunately a lot of Creationists ARE crazy, and more than a little bit brainwashed by their peers. They aren't going to believe anything that argues against the bibles word because it challenges their established believes.