There are now several known cases of species-to-species transitions that resulted in the first members of new higher taxa.
Why do gaps exist? (or seem to exist)
Ideally, of course, we would like to know each lineage right down to the species level, and have detailed species-to-species transitions linking every species in the lineage. But in practice, we get an uneven mix of the two, with only a few species-to-species transitions, and occasionally long time breaks in the lineage. Many laypeople even have the (incorrect) impression that the situation is even worse, and that there are no known transitions at all. Why are there still gaps? And why do many people think that there are even more gaps than there really are?
Stratigraphic gaps
The first and most major reason for gaps is "stratigraphic discontinuities", meaning that fossil-bearing strata are not at all continuous. There are often large time breaks from one stratum to the next, and there are even some times for which no fossil strata have been found. For instance, the Aalenian (mid-Jurassic) has shown no known tetrapod fossils anywhere in the world, and other stratigraphic stages in the Carboniferous, Jurassic, and Cretaceous have produced only a few mangled tetrapods. Most other strata have produced at least one fossil from between 50% and 100% of the vertebrate families that we know had already arisen by then (Benton, 1989) -- so the vertebrate record at the family level is only about 75% complete, and much less complete at the genus or species level. (One study estimated that we may have fossils from as little as 3% of the species that existed in the Eocene!) This, obviously, is the major reason for a break in a general lineage. To further complicate the picture, certain types of animals tend not to get fossilized -- terrestrial animals, small animals, fragile animals, and forest-dwellers are worst. And finally, fossils from very early times just don't survive the passage of eons very well, what with all the folding, crushing, and melting that goes on. Due to these facts of life and death, there will always be some major breaks in the fossil record.
Species-to-species transitions are even harder to do ent. To demonstrate anything about how a species arose, whether it arose gradually or suddenly, you need exceptionally complete strata, with many dead animals buried under constant, rapid sedimentation. This is rare for terrestrial animals. Even the famous Clark's Fork (Wyoming) site, known for its fine Eocene mammal transitions, only has about one fossil per lineage about every 27,000 years. Luckily, this is enough to record most episodes of evolutionary change (provided that they occurred at Clark's Fork Basin and not somewhere else), though it misses the most rapid evolutionary bursts. In general, in order to do ent transitions between species, you specimens separated by only tens of thousands of years (e.g. every 20,000-80,000 years). If you have only one specimen for hundreds of thousands of years (e.g. every 500,000 years), you can usually determine the order of species, but not the transitions between species. If you have a specimen every million years, you can get the order of genera, but not which species were involved. And so on. These are rough estimates (from Gingerich, 1976, 1980) but should give an idea of the completeness required.
Note that fossils separated by more than about a hundred thousand years cannot show anything about how a species arose. Think about it: there could have been a smooth transition, or the species could have appeared suddenly, but either way, if there aren't enough fossils, we can't tell which way it happened.
Discovery of the fossils
The second reason for gaps is that most fossils undoubtedly have not been found. Only two continents, Europe and North America, have been adequately surveyed for fossil-bearing strata. As the other continents are slowly surveyed, many formerly mysterious gaps are being filled (e.g., the long-missing rodent/lagomorph ancestors were recently found in Asia). Of course, even in known strata, the fossils may not be uncovered unless a roadcut or quarry is built (this is how we got most of our North American Devonian fish fossils), and may not be collected unless some truly dedicated researcher spends a long, nasty chunk of time out in the sun, and an even longer time in the lab sorting and analyzing the fossils. Here's one description of the work involved in finding early mammal fossils: "To be a successful sorter demands a rare combination of attributes: acute observation allied with the anatomical knowledge to recognise the mammalian teeth, even if they are broken or abraded, has to be combined with the enthusiasm and intellectual drive to keep at the boring and soul-destroying task of examining tens of thousands of unwanted fish teeth to eventually pick out the rare mammalian tooth. On an average one mammalian tooth is found per 200 kg of bone-bed." (Kermack, 1984.)
Do enting a species-to-species transition is particularly grueling, as it requires collection and analysis of hundreds of specimens. Typically we must wait for some paleontologist to take it on the job of studying a certain taxon in a certain site in detail. Almost nobody did this sort of work before the mid-1970's, and even now only a small subset of researchers do it. For example, Phillip Gingerich was one of the first scientists to study species-species transitions, and it took him ten years to produce the first detailed studies of just two lineages (see part 2, primates and condylarths). In a (later) 1980 paper he said: "the detailed species level evolutionary patterns discussed here represent only six genera in an early Wasatchian fauna containing approximately 50 or more mammalian genera, most of which remain to be analyzed." [emphasis mine]
Getting the word out
There's a third, unexpected reason that transitions seem so little known. It's that even when they are found, they're not popularized. The only times a transitional fossil is noticed much is if it connects two noticably different groups (such as the "walking whale" fossil reported in 1993), or if illustrates something about the tempo and mode of evolution (such as Gingerich's work). Most transitional fossils are only mentioned in the primary literature, often buried in incredibly dense and tedious "skull & bones" papers utterly inaccessible to the general public. Later references to those papers usually collapse the known species-to-species sequences to the genus or family level. The two major college-level textbooks of vertebrate paleontology (Carroll 1988, and Colbert & Morales 1991) often don't even describe anything below the family level! And finally, many of the species-to-species transitions were described too recently to have made it into the books yet.
Why don't paleontologists bother to popularize the detailed lineages and species-to-species transitions? Because it is thought to be unnecessary detail. For instance, it takes an entire book to describe the horse fossils even partially (e.g. MacFadden's "Fossil Horses"), so most authors just collapse the horse sequence to a series of genera. Paleontologists clearly consider the occurrence of evolution to be a settled question, so obvious as to be beyond rational dispute, so, they think, why waste valuable textbook space on such tedious detail?