Yes, I believe the oldest trees on Earth are around 5000 years old. Some Fungi systems could be extremely old...but they sort of clone each other so it's not exactly the same organism living...but that said most of your cells except neurons seem to die and get replaced, so continuous living is open to some interpretation. You could say the creator of the Venus Willendorf is the oldest "living in our memory" human being...the sculpture is thought to be 35,000 years old and continues to influence artists today like Jeff Koons.
http://arthistoryresources.net/willendorf/willendorfdiscover...