Curious George the monkey is most likely tail-free because he is either a bonobo or a Barbary macaque. H.A. and Margret Reys, his creators, are both deceased and never addressed this burning question.
Monkeys almost always have prehensile tails, while apes never have tails. For this reason, knowledgeable readers of the story are understandably confused by his tailless status. In the 1930s, when Curious George was created, smaller apes and even chimpanzees were often called monkeys. Though this is taxonomically incorrect, it was acceptable usage at the time. For that reason, George may be the bonobo, or dwarf chimpanzee, he most closely resembles.
He might also be a Barbary macaque. Macaques are African monkeys, but this particular species has no tail. However, since George does not resemble a Barbary macaque, it is most likely that he is a bonobo mistakenly referred to as a monkey.