The whole process of dating trees is fascinating. While no one knows which living tree is the oldest in the world, it is possible to identify trees with the oldest verifiable age, and these are conifers of one kind or another.
If you live in California you are in luck. Apparently, and unbelievably, the oldest living tree today is a bristlecone pine that is 4,600 years old, found in the White Mountains of California. Another one that was felled had 4,862 identifiable rings. The one pictured is in a grove where most of the trees are older than 4,000 years old, growing at around 10,000 ft.