Most Consecutive Games by a Met with at least 1 Run Scored
David Wright, 13 games (July 13-July 29, 2008)
Carlos Beltran, 12 games (August 17-August 30, 2006)
Derek Bell, 11 games (June 21-July 1, 2000)
Melvin Mora, 10 games (June 22-July 1, 2000)
(source: baseball-reference.com's Play Index)
Truly odd that Bell's and Mora's streaks were over the same games. In terms of the progression of this record, Frank Thomas had a six game streak in May of 1962, which was tied but not suprassed until Tommie Davis had a seven game streak in 1967, which was tied but not surpassed until Tommie Agee's 8 game streak in May of 1969, which in turn was quickly broken by Art Shamsky's 9 game streak in June/July, 1969, which was tied over the years by Mackey Sasser, Bernard Gilkey and John Olerud but not surpassed until Mora and Bell reached 10 and 11 respectively over that one sequence of games in 2000. Wright's record streak in 2008, by the way, started with the last game before the All-Star break and then proceeded with 12 straight games after the break.