No, not all monkeys have tails. While many species of monkeys do have tails that they use for balance and communication, there are some primates categorized as monkeys that do not possess tails.
Specifically, the group known as apes, which includes gorillas, chimpanzees, and orangutans, are tailless. Additionally, some species within the monkey group, such as the Barbary macaque, also lack a tail or have very short ones. The evolutionary adaptations of these primates have made tails unnecessary for their survival and locomotion in their specific environments.
Tails can provide advantages, such as aiding in balance and grasping branches in tree-dwelling species, but they are not a defining characteristic for all members of the primate order.