Yes, extinction still happens even today.
Changes in weather, occurrence of disease, environmental disasters (natural or caused by humans), and competition can all cause the extinction of life. Actually, there is evidence that throughout time, more species have become extinct than have survived.
There is no instance of a complete extinction of life on the planet. In all cases, some lineages have survived.
For example, when dinosaurs became extinct around the end of the Cretaceous period, mammals survived.
Scientists sometimes call Triceratops “the last of the dinosaurs” because its fossil remains are found in the most recent rocks containing dinosaur fossils.