I've taken the greatest players at each position to create, what in my opinion, would be the greatest baseball team of all-time.
Pitcher-Leroy Robert "Satchel" Paige

This right-handed pitcher was the greatest of all-time. The stories about his games are simply legendary. On more than one occasion he would have his outfielders all sit down, and then strikeout the other side. He would also purposely load the bases, and then show off his talents by striking out 3 consecutive batters. He started his Major League career in 1948 at 42 years old, but some people think he was even older than that. He appeared in his first MLB all-star game in 1952, making him 46 years old. He was 28-31 with a 3.29 ERA and 288 strikeouts in the Majors, but he was an old man by then. Who knows what kind of numbers he could have put up if he was allowed to play in the majors for his whole career?
Catcher-Josh Gibson

Johnny Bench and Yogi Berra are a distant second. Josh Gibson commonly referred to as the "Black Babe Ruth" was the greatest Catcher of All-Time. He never played in the Major Leagues. Only whites were allowed at that time. His official numbers are unknown. However his hall of fame plaques says he hit almost 800 homers in his 17 year career, and according to the Hall of Fame his batting average was .359 and his career slugging percentage was .648. Although it is true that some feel that his home run total is greatly exaggerated, because many of those home runs were racked up in unofficial games. Others argue that some of those unofficial games were against Major League barnstormers. He also died at the young age of 35, and he would have had even more home runs if it had not been for a tragic brain tumor. Whatever the case he is considered be one of the best, if not the best, power hitters of all-time.
1st Baseman-Lou Gehrig

There are several great 1st basemen, but none as great as the legendary Lou Gehrig. He ended his career with 493 home runs, a batting average of .340 and 1,995 RBI's. He was a 7-time all-star. He was a 2-time American League MVP (1927, 1936). He has six World Series titles. In 1934 he won the Triple Crown. He holds the MLB record for most career grand slams at 23. He holds the record for most career RBI's by a 1st baseman, highest career on base percentage by a 1st baseman .447, and highest career slugging percentage by a 1st baseman .632. He was unanimously voted into the Hall of Fame. Capping it all off, is his outstanding durability. In fact they called the "Iron Horse". He held the consecutive games played record at 2,130 until Cal Ripken Jr. broke it. There is no question that Lou Gehrig was the greatest to ever play his position.
2nd Baseman-Napoleon "Nap" Lajoie
The best 2nd basemen of all-time was Napoleon Lajoie. Some people will tell you it was Eddie Collins, Joe Morgan, or maybe Roger Hornsby, but I'm telling you it was that old Ty Cobb rival, Nap Lajoie. He ended his career with 3,242 hits and 1,504 runs. In 1901 he won the American League Triple Crown. He is only one of six players to have ever been walked when the bases were loaded. The other five were Abner Dalrymple (1881), Del Bisonette (1928), Bill Nicholson (1944), Barry Bonds (1998), Josh Hamilton (2008). He has 657 doubles which was the record when he retired, and today is the 6th highest of all-time. He was not a home runner hitter, and yet he was a 4-time league leader in slugging percentage, but what put him over the top for me, was his defense. He was the league leader in fielding six times. He was the definition of an all around player. If you're still not convinced, look at his 1901 season. He led the league in batting average (.426), OBP (.463), SLG (.643), runs (145), RBI (125), hits (232), total bases (350), doubles (48), homers (14), singles (156), runs created (158), extra base hits (76), and times on base (269). I don't think there is any 2nd baseman that can compete with Nap in his prime.
3rd Baseman-Mike Schmidt

Mike Schmidt is hands down the greatest 3rd basemen to ever play the game. He has 548home runs and 1,595 RBI's. He is a 12-time all-star, and won the National League MVP 3 times. He is a World Series champion, and a World Series MVP. He is a 10-time golden glove winner. He dominated his position, and is my pick for 3rd base.
Shortstop-Honus "The Flying Dutchman" Wagner.jpg)
Honus Wagner had a career batting average of .327, 3,417 hits, and 1,732 RBI's. He won the World Series in 1909, and was 8-time batting champion. He was one of the first five members inducted to the Hall of Fame. He received the second most votes behind Ty Cobb and tied with Babe Ruth. His rival Ty Cobb said of Wagner "Maybe the greatest star to ever take the diamond." Babe Ruth said "He was perhaps the greatest right hand hitter of all-time. Sabermatrician Bill James rates him as the second greatest player of all-time behind Babe Ruth. I am convinced that Honus Wagner was the greatest shortstop of ever.
Left Field-Barry Bonds

At Left Field I have Barry Bonds. For me it was between him and Ted Williams, but I decided to put Ted Williams as my designated hitter. I felt that for the majority of his career Barry Bonds was a better fielder. So I would prefer to have Ted as the DH. Barry Bonds is a 7-time league MVP. That is a record. He is a 12-time all-star and 8-time golden glove winner. His career batting average is .298. He has 1,996 career RBI's, 2,935 hits, 514 stolen bases, and an OBS of .444. He holds the record for most home runs in a single season at 73, and holds the record for most career home runs ever at762. He also owns the record for career walks at 2,558 and intentional walks at 688, and he may not be done. He still wants to play. Some people feel that his alleged steroid use diminishes his career. I feel that in an era where the pitchers were juiced, his numbers are still relevant.
Center Field-Willie Mays
The "Say Hey Kid" was the best center fielder of all-time. He had a career batting average of .302, 3,283 hits, and 660 home runs. He tied the record for most all-star appearances at 24. He is a 2-time MVP, and a 2-time all-star MVP. He was a 12-time golden glove winner, World Series champion, and rookie of the year. He has the most extra inning home runs, 22. He is the only player to have hit a home run in every inning 1-16. He is one of four NL players to have 8 consecutive 100 RBI season. The other three are Mel Ott, Sammy Sosa, and Albert Pujols. Willie May's first manager, Leo Durocher said of him, "He could do the five things you have to do to be a superstar: hit, hit with power, run, throw, and field." He was a superstar.
Right Field- George "Babe" Ruth

He's been called Babe, The Bambino, and The Sultan of Swat. Whatever you decide to call him, the man could play. He is often considered to be the greatest player of all-time. So then he is obviously the greatest right fielder of all-time, and no baseball team could be called the greatest without him. He batted .342. He had 2,873 career hits, and 2,217 RBI's which is the second most RBI's of all-time. He holds the records for both slugging percentage .690, and (OPS) 1.164. Babe was the best.
Designated Hitter-Ted Williams

Ted Williams was a great left fielder. He never played DH, but it would be a great spot for "The Splendid Splinter" who is commonly referred to as the greatest hitter of all-time. This team couldn't be considered the greatest team of all-time without Ted Williams. He batted .344, had 521 home runs, and 1,839 RBI's. He was a 19-time all-star and 2-time MVP. He won the Triple Crown twice. He would have had even higher numbers if it weren't for his time in the military. He is the last player to hit over .400 in a season, and he holds the highest career batting average for any player who has more than 500 home runs. He had a legendary career which ended with a home run on his last at bat. He hit for power, and he hit for average, and that is why he would be the DH on the greatest team of all-time.
This is the batting order.
1. CF Willie Mays Righty
2. SS Honus Wagner Righty
3. DH Ted Williams Lefty
4. RF Babe Ruth Lefty
5. C Josh Gibson Righty
6. 1B Lou Gehrig Lefty
7. LF Barry Bonds Lefty
8. 3B Mike Schmidt Righty
9. 2B Nap Lajoie Righty