Here's the all-time list as of the start of the 2008 season:
CAREER
AT BATS >= 1000
AVERAGE AVG AB
1 Ty Cobb .368 10591
2 Harry Heilmann .342 7297
3 Bob Fothergill .337 2444
4 Dale Alexander .331 1761
5 George Kell .325 3303
6 Placido Polanco .325 1391
7 Magglio Ordonez .325 1493
8 Heinie Manush .321 2098
9 Charlie Gehringer .320 8860
10 Hank Greenberg .319 4791
11 Gee Walker .317 3046
12 Harvey Kuenn .314 4372
13 Carlos Guillen .313 1963
14 Mickey Cochrane .313 1072
15 Barney McCosky .312 2385
16 Bobby Veach .311 5982
17 Sam Crawford .309 7985
18 Al Wingo .309 1267
19 Johnny Bassler .308 2240
20 Jim Delahanty .306 1336
21 John Stone .304 2425
22 Harry Rice .303 1174
23 Pete Fox .302 3919
24 Ivan Rodriguez .298 2080
25 Goose Goslin .297 1957
26 Al Kaline .297 10116
27 Fred Haney .297 1370
28 Ron LeFlore .297 3266
29 Topper Rigney .296 1651
30 Lu Blue .295 3394
31 Dick Wakefield .293 2128
32 Johnny Groth .293 2266
33 Jimmy Barrett .292 2259
34 Ray Boone .291 2485
35 Kid Elberfeld .290 1052
36 Hoot Evers .290 2718
37 Marty McManus .287 2314
38 Roy Johnson .287 1918
39 Vic Wertz .286 2793
40 Alan Trammell .285 8288
41 Steve Kemp .284 2504
42 Doc Cramer .282 2720
43 Rudy York .282 4677
44 Tony Phillips .281 2747
45 Mike Higgins .280 3134
46 Claude Rossman .280 1382
47 Curtis Granderson .280 1395
48 Don Kolloway .279 1335
49 Dmitri Young .279 1793
50 Larry Herndon .278 2748
51 Doc Casey .278 1060
52 Marv Owen .278 2954
53 Rusty Staub .277 2100
54 Tony Clark .277 2831
55 Lou Whitaker .276 8570
56 Willie Horton .276 5405
57 Ben Oglivie .275 1339
58 Billy Rogell .274 4418
59 Travis Fryman .274 4297
60 Kirk Gibson .273 4170
61 Bobby Higginson .272 4910
62 Norm Cash .272 6593
63 Frank O'Rourke .272 1026
64 Pat Mullin .271 2493
65 Deivi Cruz .271 2405
66 Rocky Colavito .271 2336
67 Roy Cullenbine .270 1561
68 Davy Jones .270 2173
69 Juan Encarnacion .269 1670
70 Eddie Yost .269 1018
71 Ray Hayworth .268 2006
72 Charlie Maxwell .268 2696
73 Matt Nokes .268 1246
74 Johnny Lipon .268 2272
75 Larry Woodall .268 1317
76 Robert Fick .268 1183
77 Jimmy Outlaw .268 1676
78 Jerry Priddy .267 1677
79 Jim Northrup .267 4437
80 Mike Heath .266 1353
81 Brad Ausmus .266 1207
82 George Burns .266 1756
83 Walt Dropo .266 1385
84 Bill Bruton .266 1977
85 Eddie Mayo .265 2215
86 Bob Jones .265 2990
87 Jo-Jo White .264 1800
88 Chet Lemon .263 4074
89 Lance Parrish .263 4273
90 Bill Tuttle .263 2155
91 Red Wilson .262 1479
92 Bill Freehan .262 6073
93 John Wockenfuss .261 1855
94 George Mullin .261 1423
95 Matty McIntyre .261 2997
96 Frank Bolling .261 2915
97 Brian Hunter .261 1308
98 Jackie Tavener .260 1881
99 Birdie Tebbetts .260 2058
100 Jim Delsing .260 1331
101 Damion Easley .260 3090
102 Dave Bergman .259 1967
103 Craig Monroe .259 2348
104 Cecil Fielder .258 3674
105 Gates Brown .257 2262
106 Jason Thompson .256 2204
107 Jack Warner .255 1115
108 Omar Infante .253 1592
109 George Moriarty .251 2666
110 Frank House .251 1417
111 Jake Wood .251 1860
112 Shane Halter .251 1458
113 Gary Sutherland .251 1239
114 Pat Sheridan .251 1124
115 Ralph Young .251 3158
116 Donie Bush .250 6970
117 Germany Schaefer .250 2236
118 Dick McAuliffe .249 5898
119 Mickey Tettleton .249 1887
120 Jerry Lumpe .248 1688
121 Fred Hatfield .248 1395
122 Mickey Stanley .248 5022
123 Tom Brookens .246 3543
124 Carlos Pena .244 1466
125 Don Wert .244 3800
126 Dean Palmer .244 1398
127 Boss Schmidt .243 1480
128 Joe Hoover .243 1238
129 Ossie Vitt .243 2763
130 Chico Fernandez .243 1422
131 Jimmy Bloodworth .242 1256
132 Brandon Inge .241 2914
133 Milt Cuyler .239 1270
134 Aurelio Rodriguez .239 4352
135 Darrell Evans .238 2349
136 Bill Coughlin .236 2117
137 Oscar Stanage .234 3502
138 Bob Swift .232 1690
139 Tom Veryzer .231 1183
140 Eddie Lake .229 1634
141 Gary Pettis .229 1031
142 Charley O'Leary .227 2825
143 Ed Brinkman .222 2060
144 Rob Deer .212 1164
145 Hooks Dauss .189 1124
146 Tommy Bridges .180 1003
Babe Ruth's career batting average was .342.
Ivan Rodriguez has a career batting average of .298.
Wade Boggs had a career batting average of .328 and Don Mattingly had a career batting average of .307.
As of 2009 Robinson Cano has a career batting average of .306
Keith Hernandez had a career batting average of .296. He had 2,182 career hits in 7,370 career at bats.
Babe Ruth had a career batting average of .342 with 8,398 at bats.
Through August 12, 2016, Alex Rodriguez has a career batting average of .295.
Willie Mays had a career batting average of .302, 3,283 hits in 10,881 at bats.
Sammy Sosa had a career batting average of .273.
Pete Rose's career batting average was .303 (4,256 base hits on 14,053 at bats).
Hank Aaron had a career batting average of .305 (3,771 base hits in 12,364 at bats).
Ty cobb has the highest career batting average at .366