Why Don't The Apes Continue To Evolve As Humans Now?

The simple answer is that evolution doesn't really work that way.  Species evolve because they are no longer suited to their environment, yet a very small portion of that population can survive due to some genetic flaw or differentiation.  In the case of humans, the climate changed and the rainforest gradually shifted to grasslands.  Those "apes" that were just a little better at standing on two legs (to see predators over the grass and running from them) tended to survive better and passed those traits on to their offspring.  As more and more trees disappeared, those creatures that were able to walk on two legs better, or at least stand up higher, survived.  This led to a wider hip base, which allowed larger headed creatures (bigger head, bigger brain) to survive child birth.  The cycle continued with intelligence taking over once the early hominids were established as two leg walkers.  
Furthermore, we are not direct descendants of apes.  Some people have the misconception that evolution is like a string of beads.  Some beads stay on, and others fall off.  This is not the case.  Evolution is comparable to a tree.  Apes are simply a different offshoot of the same limb from humans.  
Apes do not continue to evolve today because their is no reason for them to evolve.  The vast majority of apes are able to survive in their natural habitats without mutation, so "ape" is continually passed down from generation to generation.
Since evolution is such a slow process, it is very difficult to observe in real time.  The best example is drug resistant bacteria and viruses, though some say that is a net loss of genetic information.  If poaching of elephants continues, we may one day see a tuskless elaphant.