Since the end of the Yankee dynasty in 2000, there have been the following champions:
Cardinals (x2), Red Sox (x2), Dbacks, Angels, Marlins, White Sox, Phillies, Yankees, Giants -- nine different teams in the past 11 years.
In that same timeframe, here's the NFL:
Patriots (x3), Steelers (x2), Giants (x2), Buccaneers, Colts, Saints, Packers -- seven different teams.
NBA (starting 2001-02):
Lakers (x3), Spurs (x3), Heat (x2) Pistons, Celtics, Mavericks -- six different teams.
NHL (starting 2000-01 due to lockout):
Red Wings (x2), Avalanche, Devils, Lightning, Hurricanes, Ducks, Penguins, Blackhawks, Bruins, Kings -- ten different teams.
Here are the number of teams that missed the playoffs with nine digit payrolls since 2001. This is a slightly arbitrary endpoint, but it's easy enough.
2011 (12 teams over $100M): Red Sox (#3), Angels (#4), White Sox (#5), Cubs (#6), Mets (#7), Giants (#8), Twins (#9), and Dodgers (#12). The White Sox, Cubs, Mets, and Twins finished with losing records, Minnesota being a 98 loss team.
2010 (8 teams): Red Sox (#2), Cubs (#3), Mets (#5), Tigers (#6), White Sox (#7), and Angels (#8). Cubs, Mets, and Angels were sub-.500, Tigers 81-81. There were also a number of teams in the $90-$99M range, and only two (SF and MIN) made the playoffs.
2009 (9 teams): Mets (#2), Cubs (#3), Tigers (#5), Astros (#7). Mets finished well below .500. All three teams between $90M-$99M also missed.
2008 (10 teams): Yankees (#1), Mets (#2), Tigers (#3), Mariners (#9), and Braves (#10). Tigers and Braves below .500, Mariners lost 101 games. Cardinals (#11) and Blue Jays (#13) also missed, but the Phillies (#12) won the World Series. Tampa Bay (#29) won the American League pennant.
2007 (7 teams): Mets (#3), White Sox (#5), Dodgers (#6), and Mariners (#7). White Sox were well below .500. Tigers, Orioles, Cardinals, and Giants (#8-#12) all missed between $90M-$99M.
2006 (5 teams): Red Sox (#2), Angels (#3), White Sox (#4). Cubs, Braves, and Giants (#6-#8) missed as well, and all below .500.
2005 (3 teams): Mets (#3). Phillies (#4) missed as well.
2004 (4 teams): Mets (#4), sub-.500. Phillies, Cubs (#5-#6) also missed.
2003 (5 teams): Mets (#2), Dodgers (#4), Rangers (#5) missed. Mets and Dodgers sub-.500. Red Sox (#6, at $99.94M) made the playoffs.
2002 (4 teams): Red Sox (#2), Rangers (3), with Texas well below .500. Dodgers and Mets (#5-#6) also missed, Mets below .500.
2001 (3 teams): Dodgers (#3). Note that the Yankees payroll was a "low" $109.79M in 2001, before it began skyrocketing to $125M in 2002, $152M in 2003, $182M in 2004, and infamously topped $200M in 2005. It returned to the $200M plateau in 2008, and didn't dip back under until this season.
By my count, that's 70 teams since 2011 to spend over $100M on their roster for the season. 38 of those teams (54%) missed the playoffs. You kinda said it yourself in the opening paragraph about the very nature of baseball not guaranteeing anything - payroll included. I mean, the #2 payroll team has missed the playoffs in six out of those eleven years. The Mets have only made the playoffs once despite numerous appearances on that list.