Last made the Playoffs last season: Arizona Diamondbacks, Milwaukee Brewers, Philadelphia Phillies, Tampa Bay Rays.
Last made the Playoffs in 2010: Minnesota Twins.
Last made the Playoffs in 2009: Boston Red Sox, Colorado Rockies, Los Angeles Angels of Anaheim, Los Angeles Dodgers.
Last made the Playoffs in 2008: Chicago Cubs, Chicago White Sox.
Last made the Playoffs in 2007: Cleveland Indians.
Last made the Playoffs in 2006: New York Mets, San Diego Padres.
Last made the Playoffs in 2005: Houston Astros.
Last made the Playoffs in 2003: Florida (now Miami) Marlins.
Last made the Playoffs in 2001: Seattle Mariners.
Last made the Playoffs in 1993: Toronto Blue Jays.
Last made the Playoffs in 1992: Pittsburgh Pirates.
Last made the Playoffs in 1985: Kansas City Royals.
Until this season, the Montreal Expos/Washington Nationals hadn't made the Playoffs since 1981, or been in position to win it since the Strike of '94 wiped out a golden opportunity for them.
So half of the major league teams have made the postseason in one of the last 3 seasons, 21 out of 30 have done so in the last 5, 26 in the last 10. Only 3 have failed to do so since the 21st Century began.
Of cities with both an MLB and an NFL team:
Their MLB team has made the Playoffs more recently: New York (even if the Giants are defending World Champions), Atlanta, Baltimore, Cincinnati, Cleveland, Dallas (shocking), Detroit, Minneapolis, Oakland, Philadelphia, Phoenix, St. Louis, San Francisco, Tampa Bay, Washington (this last one last being the most shocking).
Their NFL team has made the Playoffs more recently: Boston, Chicago (more recently than the Cubs or the White Sox), Denver, Houston, Kansas City, Miami, Milwaukee (Green Bay), Pittsburgh, San Diego, Seattle.
15-10, in favor of baseball. If you want to throw in a Mets-Jets comparison, it's still 15-11 in favor of baseball. If you want to throw in the Toronto Argonauts of the CFL and compare them to the Blue Jays, it's still 15-12 in favor of baseball.