Fun; get to know each other; appreciate diversity; build institutional memory (if the stories are about the organization); identify successes to build upon/mistakes to not repeat; celebrate one team member . . .
Ask one person to tell a brief, true story or anecdote from each period of their involvement with the team. E.g., Someone who has been on the team for five years could tell five stories, something that happened relevant to the team during each year that person was a member.
Is there anything to be learned from the stories shared? Are there different versions of the same incident that someone else could tell? How could the stories have gone differently with the wisdom of hindsight? Does this have value for the team's future?
This activity could feature one person per gathering/meeting, or everyone on the team could take a turn (maybe with all focused on one year or one team event). This can also be a good way to celebrate one person only - e.g. on an anniversary of their joining the team, or on their birthday. You could ask for personal-life stories rather than team-related. The request could be for one story from every five-year or ten-years, or whatever time period is appropriate. Others could tell stories about the person, rather than the person telling their own.