See this article in the NY Times?
"It happened last fall to the Boston Red Sox' first baseman, Doug Mientkiewicz, a defensive replacement with three months of service with the team. He secured the ball that ended 86 years of torture for New England fans. He still has it, and according to an article yesterday in The Boston Globe, the Red Sox want it back."
http://www.nytimes.com/2005/01/08/sport ... oref=login
I think that he should give it back, since as a paid performer, he acquired it (unless of course, the team has a history of letting players keep the last out ball from other games). However, the idea of selling it to the Yankees has tremendous entertainment value.