Honorable Mention to the 1888-89 New York Giants (baseball). The City's 1st Pennant winners, they won 2 National League Pennants.
Honorable Mention to the 1889-90 Brooklyn Bridegrooms. Several of their players had gotten married in the 1887-88 off-season. They won the Pennant in the American Association in 1889, were admitted to the National League in 1890, and won the Pennant again.
Honorable Mention to the 1899-1900 Brooklyn Superbas. Since their manager was Ned Hanlon, who'd led the 1894-95-96 NL Champion Baltimore Orioles, and had taken some of their players (including Willie Keeler) with him, they were renamed for a famous circus troupe of the time, Hanlon's Superbas. Their Pennants, with no postseason opposition possible at the time, made this the last Brooklyn team to win baseball's World Championship for 55 years.
Honorable Mention to the 1904-05 New York Giants. Managed by John McGraw, with Christy Mathewson as pitching ace, they they won 2 National League Pennants, and the 1905 World Series, and set the standard by which New York baseball would be measured until Babe Ruth came to the Yankees. They nearly won another Pennant in 1908.
Honorable Mention to the 1911-17 New York Giants. McGraw's men won 4 Pennants in 7 years, but lost all 4 World Series. In 1911-13, they followed the 1907-09 Detroit Tigers as, to this day, the only teams ever to lose 3 straight World Series.
Honorable Mention to the 1916-20 Brooklyn Robins. Now named for their manager, Wilbert Robinson, they won the Pennant in 1916 and 1920. But, other than those 2 seasons, the team had losing records every year from 1904 to 1923.
Honorable Mention to the 1951-54 New York Giants. Maybe they didn't deserve the 1951 Pennant, but they did win the 1954 World Series, sweeping the 111-win Cleveland Indians to do it.
Honorable Mention to the 1969-73 New York Mets. 5 seasons, 2 National League Pennants and the 1969 World Championship. The '69 "Miracle Mets" remain the most beloved single-season team in the history of New York sports, ahead of even the '55 Dodgers and the '70 Knicks. Had they won Game 7 of the '73 Series, I might be tempted to put Tom Seaver, Cleon Jones and company in the Top 10.
Honorable Mention to the 1984-90 New York Mets. 7 seasons, 7 seasons finishing no worse than 2nd in the National League Eastern Division. But only 2 Division titles, 1986 and 1988; and just 1 Pennant and 1 World Series. And given all that had to happen in October 1986 for them to win that title, maybe baseball historians have been calling the wrong Met World Series win a "miracle."
Face it: Kid, Mex, Doc, Straw, Nails and the rest weren't that good. Certainly, they weren't particularly accomplished. The great Yankee teams? The '86 Mets weren't even as good as the '69 Mets.
Honorable Mention to the 2009-12 New York Yankees. 4 seasons, 3 American League Eastern Division titles, but only 1 Pennant and 1 World Championship. Brian Cashman let too many good players go, and Joe Girardi made too many pitching mistakes. This team should have won more.
10. 1933-37 New York Giants. 5 seasons, 3 National League Pennants, and the 1933 World Championship. A close call for the Pennant in 1934, and winning only 3 games against the Yankees in the '36 and 37 Series combined, prevents the team of player-manager Bill Terry, Master Mel Ott and King Carl Hubbell from being in the Top 10.
9. 1947-56 Brooklyn Dodgers. 10 seasons, 6 Pennants (plus 2 other near-misses, 3 if you extend it back to 1946), and the 1955 World Series win. The "Boys of Summer," led by Jackie Robinson, Roy Campanella and Duke Snider, were beloved, but for all they achieved, on the field and off, they never really fulfilled their promise.
That 1 title, not long before they were moved across the continent, meant that they wouldn't have been the Buffalo Bills of baseball -- but they could be considered the 1950s version of the the 1990s Atlanta Braves.
8. 1921-24 New York Giants. 4 seasons, 4 National League Pennants, 2 World Championships. John McGraw's last great team stood in the way of the Ruthian Yankees reaching baseball supremacy as long as they could, with considerably less talent than the Bronx Bombers who replaced them, their best player being Frankie Frisch.
Had they hung on in Game 7 of the 1924 World Series against the Washington Senators, they'd be a lot higher on this list -- and some of the players Frisch, as a member of the Hall of Fame's Committee on Veterans, got elected would seem like less dubious selections.
7. 1976-81 New York Yankees. 6 seasons, 4 American League Eastern Division titles, 3 AL Pennants, 2 World Championships (1977 and 1978). This was the 1st great sports team I ever watched, and it hurts a little to not be able to put them into the Top 10. And I could have... if not for the next great Yankee team, which I'm still glad I got to see.
The Bronx was burning -- with the Yankees steaming mad at each other, and taking a flamethrower to the opposition. Maybe they weren't as good as the 1927, or 1936, or 1953, or 1961, or 1998, or 2009 editions of the Pinstripes, but no baseball team in New York history ever showed more guts.
6. 1955-58 New York Yankees. 4 seasons, 4 American League Pennants, 2 World Championships -- and they other 2 World Series, they lost in Game 7. Mickey Mantle, Yogi Berra, Whitey Ford. It's not that the AL was so weak -- with 8 teams, some people called it "The Yankees and the Seven Dwarfs" -- it's that the Yankees were so good.
Making the transition from Joe DiMaggio to Mickey Mantle, this team wasn't quite as loaded as the 1936-39 version that won 4 straight, but 5 straight titles is 5 straight titles.
4. 1960-64 New York Yankees. 5 seasons, 5 straight Pennants, 2 World Championships (1961 and 1962). Led by the M&M Boys, Mickey Mantle and Roger Maris, but the aging but still effective Yogi Berra, Whitey Ford at his ace-iest, and a great infield anchored by catcher Elston Howard, teams didn't get much more effective than this. As with 1955-58, they were 2 Game 7 losses away from being so much higher.
3. 1936-43 New York Yankees. 8 seasons, 7 Pennants, 6 World Championships. It started as Joe McCarthy's team of Lou Gehrig, Bill Dickey, and the young Joe DiMaggio. It ended with Gehrig dead, and Dickey holding together a team that had seen DiMaggio, Tommy Henrich and Phil Rizzuto play, then go off to war.
Dickey went to his grave thinking that team should have won 8 straight Pennants, taking the missing one in 1940. In the 4 seasons before that, 1936 to 1939, they became the 1st team ever to win 4 straight World Series, going 16-3. The 1947 Yankees, managed by Bucky Harris, were the last gasp of this team, as they did not win the Pennant in 1948, and in 1949, under Casey Stengel, had become a different team.
2. 1921-28 New York Yankees. 8 seasons, 6 Pennants, 3 World Championships (1923, 1927, 1928). A stunning Game 7 loss in 1926 prevented a 3-peat, and may be the only thing that keeps the "Murderers' Row" Yankees of Babe Ruth and, in the latter triad of Pennants, Lou Gehrig from being an easy choice as the greatest baseball team of all time.
The 1932 Yankees won 107 games, and swept the Chicago Cubs in the World Series, but were a transition between the Ruth-Gehrig Yankees of 1926-28 and the Gehrig-Dickey-DiMaggio Yankees of 1936-39, and thus aren't included here.
1. 1996-2003 New York Yankees. 8 seasons, 6 Pennants, 4 World Championships (1996, 1998, 1999 and 2000). This team could beat you with contact hitting and power hitting, in each case to the opposite field. It could beat you with good baserunning. It could beat you with great starting pitching and with even better relief pitching. And it could beat you with defense.
The traditional argument for the Islander dynasty is their 19 straight postseason series won. Well, 16 teams qualify for the NHL Playoffs. In MLB in this era, 8 teams did, meaning that, for 8 years, the Yankees had a maximum of 24 rounds, and they went 16-4 -- including 11-0 from the 1998 AL Division Series to the 2001 AL Championship Series. They went 11-2 in the '98 postseason, and 11-1 in '99. They didn't care about home-field advantage: Over those 8 years, their postseason record was 32-16 at home and 29-15 on the road.
Their conquests included perhaps the most talented teams ever put together by the franchises of the Texas Rangers, the Boston/Milwaukee/Atlanta Braves, the Cleveland Indians, the San Diego Padres, and the Seattle Mariners. They included a Mariner team that tied the MLB record with a 116-win regular season; a very motivated Met team that finally got the franchise's 1st Subway Series, only to get outwitted by the Yankees 4 games out of 5; and, in 1999 and 2003 if not 2004, an even more motivated Boston Red Sox team.
You say that Yankee team used steroids? Look at the teams they played: The 1996-99 Rangers, the 1996-97 Baltimore Orioles, the 2000-01 Oakland Athletics, the 2000 Mets (don't tell me Mike Piazza was taking acne medication), and, of teams that actually beat them, the 2001 Arizona Diamondbacks, the 2003 Florida Marlins, and the 2004 Red Sox. The Yankees were no less "legitimate" than their opponents.
Whether the Joe Torre Era Yankees will turn out to be the last baseball dynasty remains to be seen. But the evidence suggests that they are the greatest sports team in the history of the New York Tri-State Area, and possibly the greatest baseball team ever.