Tim Wakefield threw 169 pitches on 6/5/1997, shattering the Red Sox record. He came one out short of a complete game, and the Red Sox won 2-1.

No surprise here. Ted Williams has the highest ever season OPS for a Red Sox player. His OPS was 1.288 in 1941, the same year he batted .406. 

Nomar Garciaparra was intentionally walked in four games from 8/19/2000 through 8/22/2000, the most consecutive games any Red Sox player has been intentionally walked.

John Tudor picked off three batters on 5/30/1982. The Red Sox lost the game by a score of 1-2.

In 1939, Jim Bagby pitched 80 innings and gave up 63 earned runs, posting an ERA of 7.09—the highest of any Red Sox pitcher who threw more than 80 innings.

Spike Owen owns the Red Sox record for the most runs scored in a single game, and is tied for the Major League record. Owen scored six runs on 8/21/1986 vs. the Cleveland Indians. He scored each time he reached base, finishing 5 for 6 with a base on balls.

The Red Sox won the game by a score of 24-5.

Cy Young threw forty-one complete games for the Boston Americans in 1902. He pitched 384.2 innings that year, ending the season with a 32-11 record, a 2.15 ERA, and 1.048 WHIP.

Jerry Remy stole four bases on 6/14/1980 against the Angels—the most any Red Sox player has swiped in a single game.

Derek Lowe pitched in 323 games (676.1 innings) without picking off a batter. His streak spanned over five and a half years, from 9/1/1997 until 4/25/2003.

In 1999, Pedro Martinez threw 213.1 innings and gave up only 37 walks—the smallest season total for any Red Sox pitcher who threw more than 200 innings.

Nomar Garciaparra owns the Red Sox record for hitting a triple in the most consecutive games. His four game streak ran from 5-31-2003 through 6-04-2003.

Remarkably, he started another triple streak six days later, hitting one in three straight games—good enough to put him in a tie for second place with Wade Boggs, Jim Rice and Lenny Green.

Oldest player to have a season OPS above 1.000

In 1960, Ted Williams posted an OPS of 1.096. He was 41 years old.

note: For the sake of sample size, I only included batters with more than 200 at bats in my query. Williams had 310.