Why aren't there any transitional animals today?
Every species on the planet is "transitional" - this is because there is no ultimate or final species. Species branch out from one another, sometimes species go extinct, leaving gaps between the extant branches. But it also comes down to how you look at it; if you were comparing blue whales and humans, then chimpanzees (and many other species) would be "transitional", so some "transitional" species are extant, others are extinct. In fact, it is estimated that 1% of species that have ever existed are extant, the remaining 99% are extinct. 

It's very hard to say why the "transitional" species of chimpanzees and humans went extinct. There's a lot of (sub-)species that would fall in that bracket, thus to answer that specifically would be too broad and speculative for this site.



Some concepts and key points


Speciation is a gradual process with species forming over time out of one in to two (or more). 
Species is a hard concept to pin down because it applies binary/categorical classification to a very much continuous distribution 
Evolution is a process of change, and in all likelihood it will be an unceasing process because at least one of the mechanisms will likely be affecting every species in some way. This means that every species is "transitional" because no species represents an end point.