Well there will be several answers to this question.
The first answer is that we really will never know. In absolute terms, there may well have been someone who lived & died at an incredible age but no records were kept, so we just do not know.
The second answer is that many of the record holders are very suspect, because there was no one still alive that really knows when they were born & record keeping over 100 years ago is always a bit suspect.
There are certainly many well documented people in the 100-110 years range and a few up to 115. Jiroemon Kimura was a Japanese man who lived to be age 116 years and died May 6th 2013.
The third answer is that your question could mean alive today or it could be who lived the longest & then died & in that case, it would again be Mr Kimura.
The ancients claimed that a Biblical fellow named Methuselah, lived to be 969 years old, but that is subject to the interpretation of how long a year was to the ancient people. We know they didn't have a calendar so we don't know how his age was documented.