If you are talking about pitchers and who has the most K's, the answer is Nolan Ryan with 5,714 strikeouts. If you are talking about batters who have struck out at the plate, the leader is Reggie Jackson with 2,597 strikeouts.
Nolan Ryan holds the record for most career strikeouts with 5.714.
Derek Jeter holds the all-time record for most strikeouts by a Yankees player.
Ryan Howard holds the record for most strikeouts for a batter in a World Series with 13 in 2009. Bob Gibson holds the record for most strikeouts for a pitcher with 35 in 1968.
Nolan Ryan, with 5,714 strikeouts, holds the career record.
Mark Reynolds with 223 holds the major league record.