Trees can live for a long time. We have lost some perspective on this due to modern plantation forest logging practices.
In Australia, softwoods (e.g. pine) are usually grown in plantations. Trees harvested for logs from a pine plantation are typically logged at 20 to 30 years of age (more information on how to age trees is here).
Approximately 87% of Australian hardwoods (e.g. eucalypts) are harvested from native forests (source). The trees age, at the time of logging, is between 30 and 120 years .
Old growth Australian eucalypt forests can be 200-300 years old but rarely exceed 350 years of age due to forest fires. Old growth redwood trees in on the US west coast are typically 500-700 years of age, with some trees up to 2000 years old (https://www.nps.gov/redw/faqs.htm).
Bristlecone pines, which also grow in many parts of western USA get even older. Below is a tree named "Methuselah" that is 4,765 years old!
If you think that is old, there are several "clonal" colonies — which are made up of genetically identical trees connected by a single root system — that are much older. The tree below, named "Old Tjikko", is about 9550 years old.
Another amazing "tree" in the colony of Quaking Aspen that is all part of one 80,000 year old root system. The colony is made up of 40,000 genetically identical trunks connected to one single common root system. It is called the Pando or Trembling Giant and is located in Utah in the USA.
The Trembling Giant;-
The trees above help to put some perspective on what we call "old". For many trees, a few hundred years is just a short space of time.