Here's the all-time list as of the start of the 2008 season:
CAREER
RUNS R
1 Craig Biggio 1844
2 Jeff Bagwell 1517
3 Cesar Cedeno 890
4 Jose Cruz 871
5 Jimmy Wynn 829
6 Lance Berkman 782
7 Terry Puhl 676
8 Bob Watson 640
9 Bill Doran 611
10 Joe Morgan 597
11 Enos Cabell 522
12 Doug Rader 520
13 Ken Caminiti 496
14 Kevin Bass 465
15 Richard Hidalgo 442
16 Glenn Davis 427
17 Roger Metzger 407
18 Brad Ausmus 400
19 Derek Bell 386
20 Craig Reynolds 373
21 Denny Walling 351
22 Luis Gonzalez 344
23 Phil Garner 337
24 Bob Aspromonte 336
25 Morgan Ensberg 323
26 Steve Finley 301
27 Rusty Staub 297
28 Alan Ashby 282
29 Billy Hatcher 279
30 Denis Menke 269
31 Moises Alou 265
32 Adam Everett 257
33 Gerald Young 249
34 Bill Spiers 241
35 Art Howe 228
36 Dickie Thon 226
37 Julio Lugo 222
38 Lee May 211
39 Greg Gross 204
40 Mike Lamb 194
41 Johnny Edwards 181
42 Tony Eusebio 179
43 Rafael Ramirez 175
44 Jesus Alou 174
T45 Brian Hunter 173
T45 Jeff Kent 173
47 Al Spangler 172
48 Ricky Gutierrez 171
49 Willy Taveras 167
50 Jason Lane 165
51 Norm Miller 163
52 Eric Anthony 159
53 Carl Everett 158
54 Jose Vizcaino 154
T55 Sonny Jackson 151
T55 Bob Lillis 151
57 Andujar Cedeno 150
58 James Mouton 149
59 Chris Burke 148
60 Wilbur Howard 146
61 Cliff Johnson 142
62 Sean Berry 140
63 John Bateman 139
64 Jerry Mumphrey 135
65 Ray Knight 130
66 Tommy Helms 128
67 Tim Bogar 118
68 Casey Candaele 113
69 Carl Warwick 112
70 Daryle Ward 110
71 Walt Bond 109
72 Eric Yelding 108
73 Mark Bailey 100
74 Rafael Landestoy 99
75 Geoff Blum 96
76 John Cangelosi 95
T77 Tony Scott 93
T77 Carlos Lee 93
79 Luke Scott 86
T80 Orlando Miller 82
T80 Roman Mejias 82
T82 Jeffrey Leonard 79
T82 Joe Ferguson 79
T82 Julio Gonzalez 79
T85 Lee Maye 76
T85 Milt May 76
87 Ron Davis 75
88 Orlando Merced 74
T89 Scott Servais 71
T89 Rob Andrews 71
T91 Larry Milbourne 70
T91 Carlos Beltran 70
93 Ron Brand 68
94 Chuck Harrison 67
95 Curt Blefary 66
96 Orlando Palmeiro 65
T97 Eric Bruntlett 63
T97 Eddie Kasko 63
T99 Vinny Castilla 62
T99 Joe Gaines 62
T99 Jim Pankovits 62
T99 Mark Loretta 62
103 Franklin Stubbs 59
T104 Norm Larker 58
T104 Hector Torres 58
106 Hunter Pence 57
107 Roger Cedeno 54
T108 Glen Barker 53
T108 Mitch Meluskey 53
T108 Derrick May 53
T111 Luis Pujols 50
T111 Glenn Wilson 50
113 Eddie Taubensee 49
T114 Omar Moreno 48
T114 Nellie Fox 48
116 Julio Gotay 46
T117 Dave Magadan 44
T117 Joe Pepitone 44
T117 Joey Amalfitano 44
T120 Harry Spilman 43
T120 Mike Simms 43
T122 Rick Wilkins 40
T122 Preston Wilson 40
T124 J.R. Richard 39
T124 Chris Truby 39
T124 John Mayberry 39
T124 Eddie Mathews 39
T128 Larry Dierker 38
T128 Jim Gentile 38
T128 Pete Runnels 38
T131 Russ Johnson 37
T131 Alex Trevino 37
T131 Howie Goss 37
T134 Don Wilson 36
T134 Johnny Temple 36
T134 Dave Nicholson 36
T134 Larry Howard 36
T138 Ken Boswell 35
T138 Mike Hampton 35
T140 Chris Donnels 34
T140 Jerry Davanon 34
T140 Chuck Carr 34
T140 Ernie Fazio 34
T140 Shane Reynolds 34
T140 Skip Jutze 34
146 Hal Smith 33
T147 Dave Bergman 32
T147 Leon Roberts 32
T147 Joe Niekro 32
T150 Aubrey Huff 31
T150 Pete Incaviglia 31
T152 Tommie Agee 30
T152 Jim Pendleton 30
T152 Mike White 30
T152 Marty Martinez 30
T156 Mark Davidson 29
T156 Bob Knepper 29
T156 Bob Gallagher 29
159 Danny Heep 28
160 Gregg Zaun 27
T161 Tommy Davis 26
T161 Cesar Geronimo 26
T161 Merritt Ranew 26
T161 Mike Scott 26
T161 Jerry Grote 26
T166 Jimmy Sexton 25
T166 Nolan Ryan 25
T166 Dick Simpson 25
T169 Tom Griffin 24
T169 Thomas Howard 24
T169 Eric Munson 24
T169 Raul Chavez 24
T169 Buddy Bell 24
T169 Ty Wigginton 24
T175 Dave Giusti 23
T175 Craig Shipley 23
T175 Bobby Abreu 23
T175 John Mizerock 23
T179 Pete Harnisch 22
T179 Ed Herrmann 22
T181 Jimmy Stewart 20
T181 Darryl Kile 20
T181 Matt Mieske 20
T181 Wade Miller 20
T185 Jim Landis 19
T185 Bob Bruce 19
T185 Milt Thompson 19
T185 Karl Rhodes 19
T185 Bruce Bochy 19
T185 Roy Oswalt 19
T185 Chris James 19
T185 Tony Walker 19
T185 Gary Geiger 19
T194 Gary Woods 18
T194 Jack Hiatt 18
T194 Carroll Hardy 18
T194 Bert Pena 18
T198 Sandy Valdespino 17
T198 Ken Oberkfell 17
T200 Ken Forsch 16
T200 Paul Bako 16
T200 Joaquin Andujar 16
T200 Jose Lima 16
T200 Felix Mantilla 16
T200 Andy Stankiewicz 16
T206 Davey Lopes 15
T206 Jim Campbell 15
T206 Doug Drabek 15
T206 Dave Roberts 15
T210 Lee Thomas 14
T210 Ray Montgomery 14
T210 Javier Ortiz 14
T210 Kiko Garcia 14
T210 Mark Portugal 14
T210 Tim Tolman 14
T210 Louie Meadows 14
T210 Scott Loucks 14
T210 Turk Farrell 14
T210 Jim Beauchamp 14
T210 Willie Crawford 14
T221 Pat Listach 13
T221 Mike Cuellar 13
T221 J.C. Hartman 13
T221 Rich Chiles 13
T221 Brandon Backe 13
T226 Dave Clark 12
T226 Ty Gainey 12
T226 Stan Javier 12
T226 Vern Ruhle 12
T226 Alan Knicely 12
T226 Dave Roberts 12
T226 Chris Holt 12
T226 Billy Goodman 12
T226 Bill Heath 12
T226 Jerry Reuss 12
T226 Phil Plantier 12
T237 Dave Rohde 11
T237 Aaron Pointer 11
T237 Joe Pittman 11
T237 Danny Darwin 11
T237 Rick Parker 11
T242 Josh Anderson 10
T242 Chuck Jackson 10
T242 Randy Knorr 10
T242 Mike Felder 10
T242 Art Gardner 10
T242 Jim Deshaies 10
T242 Keith Lampard 10
T242 Carl Nichols 10
T242 Don Buddin 10
T242 Humberto Quintero 10
T252 J.R. Towles 9
T252 Cody Ransom 9
T252 Jimmy Jones 9
T252 Dave Adlesh 9
T252 Brock Davis 9
T252 Jose Herrera 9
T252 Wandy Rodriguez 9
T252 Kenny Lofton 9
T260 Scott Elarton 8
T260 Juan Guerrero 8
T260 Pidge Browne 8
T260 George Bjorkman 8
T260 Ken Johnson 8
T260 Don Nottebart 8
T260 Gary Sutherland 8
T260 Ollie Brown 8
T260 Denny Lemaster 8
T260 Greg Swindell 8
T260 Nate Colbert 8
T271 Ivan Murrell 7
T271 Frank Thomas 7
T271 Chris Jones 7
T271 Sean Bergman 7
T271 Todd Self 7
T271 Jim Golden 7
T271 Jackie Brandt 7
T271 Sid Bream 7
T271 Johnny Weekly 7
T271 Bobby Fenwick 7
T271 Scooter Tucker 7
T271 Wade Blasingame 7
T283 Floyd Bannister 6
T283 Hal King 6
T283 J.R. Phillips 6
T283 Rob Sperring 6
T283 Jack Howell 6
T283 Jose Tolentino 6
T283 Ray Busse 6
T283 Dan Larson 6
T283 Mark McLemore 6
T292 Leon McFadden 5
T292 Kirt Manwaring 5
T292 Reggie Baldwin 5
T292 Gus Triandos 5
T292 Tim Redding 5
T292 Steve Lombardozzi 5
T292 Colin Porter 5
T292 Chris Sampson 5
T292 Ernest Riles 5
T292 Alan Zinter 5
T292 Keith Drumright 5
T292 Jim Fuller 5
T292 Dan Driessen 5
T292 Peter Munro 5
T292 Andy Pettitte 5
T292 Ronn Reynolds 5
T292 Dave Campbell 5
T292 Donne Wall 5
T292 Jack Billingham 5
T292 Mark Lemongello 5
T312 Jim Clancy 4
T312 Andy Mota 4
T312 Charlie Hayes 4
T312 Joe Sambito 4
T312 John Paciorek 4
T312 Phil Nevin 4
T312 Don Sutton 4
T312 Dave Roberts 4
T312 Benny Distefano 4
T312 Al Heist 4
T312 Claude Osteen 4
T312 Don Bryant 4
T312 Jeriome Robertson 4
T312 Ron Villone 4
T312 Mike LaCoss 4
T312 Joe Cannon 4
T312 Lee Bales 4
T312 Jose Uribe 4
T312 Dave Mlicki 4
T312 Carlos Hernandez 4
T312 Hal Brown 4
T312 Rich Gedman 4
T312 Steve Henderson 4
T312 Claude Raymond 4
T312 Mick Kelleher 4
T312 Keith Ginter 4
T312 Jim Ray 4
T312 Brian Williams 4
T312 George Culver 4
No , Sachin Tendulkar holds the record of maximum runs in a test career which is over 13000
The Mets team record for runs scored by a player in a game is 6 by Edgardo Alfonso in a game against the Astros on August 30, 1999.
Lou Gehrig scored 1,888 runs in his career.
Mickey Mantle with 42 runs scored in 12 World Series.
The all time leader in runs scored is Ricky Henderson with over 2,000 runs in his career, but the record for the most runs scored in one season is 190 set by Babe Ruth.
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Through August 12, 2016, Alex Rodriguez had scored 2,021 runs during his career.
7700
Edgardo Alfonso holds the record with 6 hits against the Houston Astros on August 30, 1999. In that game he also set the team record for most runs scored in a game with 6 and tied the team record for home runs in a game with 3.
This year,he had scored 1,690 runs for his career plus,reaching 17,0000!
Cal Ripken Jr. had 1,647 career runs scored.
The most runs the Astros have scored in a game is 19 against the Pirates on May 11, 1999. The Astros won 19-8.