Sometimes people who don't believe in evolution ask, "Why aren't there any intermediate species?"
I always used to think they meant why aren't there any intermediate species in the fossil record. And that was usually followed by the thought that where a good fossil record exists, there are intermediate species (now extinct). And so the question always seemed silly. Not to mention that the fossil record is very incomplete in most places and so the path of evolution does seem gappy, set aside the fact that related but different species often didn't live in the same places (geographical separation is in fact one of the factors that CAUSES speciation).
But then I started reading Richard Dawkins' "The Blind Watchmaker" and it occurred to me that this question, usually from people with a creationist biblical perspective, is really better interpreted as, "Why aren't there any intermediate species alive today?"
Set aside the fact that "intermediate species" is a relative term (could not chimps be considered an intermediate species between humans and orangutans, for example, from a morphological perspective?), the reason that we don't see too many intermediate species alive today (and there are some, like many kinds of plants that can hybridize), is because the evolutionary tree branches in TIME.
Chimps and humans have a common ancestor. But when that ancestor lived, perhaps 5 million years ago, there were not yet any chimps or humans. When that species branched, both branches began to CHANGE from the ancestral species, one becoming chimps and one becoming humans.
But once the split occurred and the two species could no longer interbreed, the ancestral species ceased to exist.
But fossils of the ancestral species do exist, dated between 5-7 million years ago. In fact, there are three possible candidates - Ardipithecus, Sahelanthropus, or Orrorin.
Such fossils are rare and incomplete, which makes determining which may have been the closest ancestral common ancestor of chimps and humans difficult. In fact, none of the fossils found is probably THE common ancestor (mathematically, there can only be ONE actual individual that serves as the branch point for the evolutionary tree).
So I hope this helps to answer the question about where are the intermediate species. Where they exist, they are probably incomplete and still buried in rocks. In plants, we know that related subspecies can still hybridize, such as maize and corn, as well as numerous varieties of flowering plants. That's good, because plant fossils are even rarer than the fossils of bony animals.
On the distantly related question of how could a single celled organism eventually lead to the multicellular complexity of a human being...you need look no further than this very occurrence during embryonic development from a single-celled fertilized egg to a new born baby.
Ontogeny recapitulates phylogeny.