National League teams won 11 times, American League teams won 9.
No team won back-to-back World Series, and only four teams had back-to-back league pennants (two losing twice, two going 1–1).
The Red Sox won 4, Giants won 3, Cardinals won 2, and 11 different teams won 1. Six teams lost twice. It's also the first 20-year period in which the Yankees only won one World Series since the first 20 year window (Yankees first win was 1923).
Red Sox–Cardinals was the only repeat matchup. (The previous 20 series also had a single repeat, Yankees–Braves. The previous 20 featured three between the Yankees and Dodgers and two Orioles–Pirates Series. The 20 before that, the Yankees faced the Dodgers 7 times and the Giants, Braves, and Cardinals twice each.)
Several teams won their first World Series in franchise history or their first Series after a 30+ year drought: Chicago Cubs after 108 years, Chicago White Sox after 88 years, Boston Red Sox after 86 years, San Francisco Giants after 56 years (first since move from New York), Dodgers after 32 years, Royals after 30 years; Houston Astros in their 56th year, Los Angeles Angels in their 42nd year, Arizona Diamondbacks in their 4th year. Additionally, the Philadelphia Phillies became the final of the original 16 MLB franchises to win a second World Series.
20 teams made at least one appearance. Every expansion team made an appearance except four: the Mariners, Brewers, Blue Jays, and Padres. This period contained the first World Series appearance by the Angels, Astros, Diamondbacks, Nationals, Rays, and Rockies.
Of original 16 MLB franchises, only six didn't appear at least once in the last 20 Series: Athletics, Braves, Orioles, Pirates, Reds, Twins.
Seven Series went 7 games, four went 6 games, five went 5 games, four were swept in 4 games. The Nationals became the first team to win all four road games and lose all three home games. In four championships, the Red Sox lost a total of three games.
10 of the 40 pennants in this period were won by a wild card team; 6 wild card teams won the Series, and two World Series featured two wild card teams. I suspect the wild card expansion (now four teams per league are in the playoffs) have contributed to the recent diversity in appearances and victories: a team that's performing really well late in the year now has more chances to beat an established team that got a big division lead early but didn't finish as strong.