Drawing on the Play Index at Baseball-Reference.com, I discovered the following bests for major-league hitters aged 40 and older:
Most games played — Pete Rose, 732
Most games in starting lineup — Pete Rose, 643
Most plate appearances — Pete Rose, 2955
Most at-bats — Pete Rose, 2574
Most runs — Sam Rice, 327
Most hits — Pete Rose, 699
Most doubles — Sam Rice, 95
Most triples — Honus Wagner, 36
Most home runs — Carlton Fisk, 72
Most runs batted in — Carlton Fisk, 282
Most stolen bases — Rickey Henderson, 109
Most times caught stealing — Rickey Henderson, 34
Most times walked — Pete Rose, 320
Most times struck out — Julio Franco, 336
Highest batting average — Ty Cobb, .343*
Highest on-base percentage — Barry Bonds, .464*
Highest slugging percentage — Barry Bonds, .561*
Highest on-base-plus-slugging percentage (OPS) — Barry Bonds, 1.025*
Most sacrifice hits (bunts) — Honus Wagner, 45
Also of note:
Babe Ruth had only 6 home runs as a 40-year-old in his final (partial) season, as a member of the Boston Braves.
Ted Williams is remembered as a great “old” player, and he was. But his 40-and-over record (compiled in 1959-60) is almost matched by that of his great contemporary, Stan Musial (whose 40-and-older record was compiled in 1961-63):
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* In each case, this excludes players with small numbers of plate appearances (always fewer than 20). Also, David Ortiz has a slugging average of .652 and an OPS of 1.067 for the 2016 season (his first as a 40-year-old), but the season isn’t over.