NOTrees have to grow constantly in order to repair their tissues, so every year the trunk has to get thicker. Eventually the trunk becomes too large to allow any further growth and the tree dies. So trees have an absolute maximum lifespan, just like people.
Having said that, many trees are capable of vegetative propagation, where they produce new genetically identical individuals form their roots or branches. However these new plants are just clones, the original tree still dies.