Baseball Reference (Linked at the bottom) has a feature by which you can sort every major leaguer according to the state where they were born. Using that feature I've built the All Louisiana team.
DH Rusty Staub, New Orleans (1944), Career 1963-1985: Six All-Star appearances, 1,466 RBI (43rd), 2,716 hits (50th).
C Bill Dickey (HOF), Bastrop (1907), Career 1928-1946: Yankee catcher mentored Yogi Berra. 11 All-Star appearances, 5 top-10 MVP finishes. Would have several Gold Gloves had ther been such a thing.
1B Will Clark, New Orleans, (1964), Career 1986-2000: 6 All-Star appearances, 1 Gold Glove, career .303 average. Peak season 1989 with .333 average, 23 homers, 111 RBI while leading Giants to NL pennant.
2B Connie Ryan, New Orleans (1920), Career 1942-1954: Default selection, as the state is weak at this position (same thing for short stop and third base). Made one All-Star team in 1944 as a Boston Brave.
3B Odell Hale, Hosston (1908), Career 1931-1941: Career .289 hitter with two 100 RBI seasons for the Indians.
SS George Strickland, New Orleans (1926), Career 1950-1960: Must have been a good glove man because there are no offensive highlights in the stats.
LF Albert Belle, Shreveport (1966), Career 1989-2000: Degenerative hip problem ended a brilliant career for a dispicable guy. Did make 5 All-Star teams. It's hard to pick his best season; in 1995 he hit .317 with 50 home runs and 126 RBI, in 1996 he hit .311 with 48 and 148, and in 1998 he batted .328 with 49 and 152. He had more great season than just those too.
CF Reggie Smith, Shreveport (1945), Career 1966-1982: 7 All-Star selections, 1 Gold Glove. Career .287 hitter with 2,020 hits.
RF Mel Ott (HOF), Gretna (1909), Career 1926-1947: 12 All-Star teams. led NL in home runs 6 times totaling 511 for his career (18th). 1,860 RBI's is 10th on the all-time list. First ballot Hall of Famer was player/manager for the New York Giants during his last seven seasons.
SP1 Ted Lyons (HOF), Lake Charles (1900), Career 1923-1946: Only one All-Star appearance, but 21-year career resulted in 260 career wins, including three 20-win seasons for a White Sox team that never made the postseason while Lyons was there. Also managed team from 1947-1949.
SP2 Vida Blue, Mansfield (1949), Career 1969-1986: 6 All-Star appearances and 209 wins. Won Cy Young and MVP for A's in 1971 when he went 24 and 8, with 8 shutouts, 301 strikeouts in 312 innings, and a 1.82 ERA on a Championship team.
SP3 Ron Guidry, Lafayette (1950), Career 1975-1988: 4 All-Star teams, 5 Gold Gloves, and 6 Cy Young top-10's. Won Al Cy Young with Yankees in 1978 by going 25 and 3, with 9 shutouts, 248 K's, and a 1.74 ERA. Guidry went 3 and 1 with a 1.69 ERA in 4 World Series starts.
SP4 Andy Pettitte, Baton Rouge (1972), Career 1995-present: A little over half way through his career he's 149 and 78. Pettitte is known as a big-game pitcher for the Yankees. He's about four more good seasons away from being a sure-fire Hall of Famer.
SP5 Chuck Finley, Monroe (1962), Career 1982-2002: Always good but never great, Finley did not pitch in 2003, but don't rule out a return in 2004. At this point he's made 5 All-Star teams and won 200 games.
CL Lee Smith, Shreveport (1957), Career 1980-1997: 7 All-Star appearances, 3 Reliever of the Year awards, 4 Cy Young top-10's. Led his league in saves 4 times and ended his career with more saves than anybody else (478); should be a Hall of Famer someday.
Other Noteables
1B Joe Adcock, Coushatta (1927), Career 1950-1966: 1 All-star selection, 1,832 hits, 336 home runs.
CF Vernon Wells, Shreveport (1978 just like me), Career 1999 - present: Made first All-Star team in 2003. Good in 2002, absolutely fantastic in 2003 leading the AL in hits (215), doubles (49), and total bases (373).
SP J.R. Richard, Vienna (1950), Career 1971-1980: Strange career ended by a stroke in 1980, but for four years (1976-1979) he was arguably the best pitcher in the NL.
Less detailed state teams below
All Arkansas
DH Lloyd Moseby, Portland (1959), 1980-1991: 1-time All-Star
C Sherm Lollar, Durham (1924), 1946-1963: 7-time All-Star
1B Tommy McCraw, Malvern (1940), 1963-1975: 0-time All-Star
2B George Kell (HOF), Swifton (1922), 1943-1957: 10-time All-Star
3B Brooks Robinson (HOF), Little Rock (1937), 1955-1977: 15-time All-Star
SS Arky Vaughn (HOF), Clifty (1912), 1932-1948: 9-time All-Star
LF Lou Brock (HOF), El Dorado (1939), 1961-1979: 6-time All-Star
CF Willie Davis, Mineral Springs (1940), 1960-1979: 2-time All-Star
RF Rick Monday, Batesville (1945), 1966-1984: 2-time All-Star
SP1 Dizzy Dean (HOF), Lucas (1910), 1930-1947: 4-time All-Star
SP2 Johnny Sain, Havana (1917), 1942-1955: 3-time All-Star
SP3 Lon Warneke, Mt. Ida (1909), 1930-1945: 5-time All-Star
SP4 Preacher Roe, Ash Flat (1915), 1938-1954: 5-time All-Star
SP5 Hank Wyse, Lunsford (1918), 1942-1951: 1-time All-Star
CL Ellis Kinder, Atkins (1914), 1946-1957: 0-time All-Star
Also Noteable: SS Travis Jackson (HOF), Waldo (1903), 1922-1936: 1-time All-Star
All Texas
DH Don Baylor, Austin (1949), 1970-1988: 1-time All-Star
C Gus Mancuso, Galveston (1905), 1928-1945: 2-time All-Star
1B Cecil Cooper, Brenham (1949), 1971-1987: 5-time All-Star
2B tie Joe Morgan (HOF), Bonham (1943), 1963-1984: 10-time All-Star
2B tie Rogers Hornsby (HOF), Winters (1896), 1915-1937: 2 NL Triple Crowns
3B Eddie Matthews (HOF), Texarkana (1931), 1952-1968: 9-time All-Star
SS Ernie Banks (HOF), Dallas (1931), 1953-1971: 11-time All-Star
LF Frank Robinson (HOF), Beaumont (1935), 1956-1976: 12-time All-Star
CF Curt Flood, Houston (1938), 1956-1971: 3-time All-Star
RF Tris Speaker (HOF), Hubbard (1888), 1907-1928: 1 AL MVP, .345 career hitter
SP1 Greg Maddux, San Angelo (1966), 1986-present: 8-time All-Star
SP2 Nolan Ryan (HOF), Refugio (1947), 1966-1993: 8-time All-Star
SP3 Hippo Vaughn, Weatherford (1888), 1908-1921: Pitcher Triple Crown in 1918
SP4 Schoolboy Rowe, Waco (1910), 1933-1949: 3-time All-Star
SP5 Doug Drabek, Victoria (1962), 1986-1998: 1-time All-Star
CL Firpo Marberry, Streetman (1898), 1923-1936: 148 Wins, 101 Saves
All Pacific Northwest
*Only 23 MLB players from Idaho ever
DH Dave Kingman, Pendleton, OR (1948), 1971-1986: 3-time All-Star
C Sammy White, Wenatchee, WA (1928), 1951-1962: 1-time All-Star
1B John Olerud, Seattle, WA (1968), 1989-present: 2-time All-Star
Ryne Sandberg, Spokane, WA (1959), 1981-1997: 10-time All-Star
Ron Santo, Seattle, WA (1940), 1960-1974: 9-time All-Star
SS Vance Law, Boise, ID (1956), 1980-1991: 1-time All-Star
LF Harmon Killebrew (HOF), Payette, ID (1936), 1954-1975: 11-time All-Star
CF Dale Murphy, Portland, OR (1956), 1976-1993: 7-time All-Star
RF Earl Averill (HOF), Snohomish, WA (1902), 1929-1941: 6-time All-Star
SP1 Mickey Lolich, Portland, OR (1940), 1963-1979: 3-time All-Star
SP2 Larry Jackson, Nampa, ID (1931), 1955-1968: 4-time All-Star
SP3 Vern Law, Meridian, ID (1930), 1950-1967: 1-time All-Star
SP4 Todd Stottlemeyer, Sunnyside, WA (1965), 1988-present: 138 wins
Gerry Staley, Brush Prairie, WA (1920), 1947-1961: 3-time All-Star
CL Randy Myers, Vancouver, WA (1962), 1985-1998: 4-time All-Star