It's pretty easy to look at the seventeen consecutive losing seasons that the Pirates have put up, or the perennial 90-100 loss teams that the Expos/Nationals have keep fielding, or any of the other string of lousy teams that exist today and think only about their failures as a franchise. We've seen the Royals be bad for so long, for example, that some of us don't even remember a time when they were good.
But of course it's a silly thing to be stuck on the present like that. Major League Baseball has been around for well over a century, and even the most recent franchises have nearly 15 years under their belts. With so much history, it's virtually guaranteed that each franchise is the best at something.
In fact, to prove it, here is a list of all thirty teams and one single-season record that the team, or a member of the team, owns. All-time franchise records, like most World Series championships or most losses, aren't included. With some franchises being 130 years old and some only 13, that didn't seem fair. Instead, the list counts single-season records set by a player (or group of players) while wearing the uniform. Most home runs in a season, then, is considered a Giants record, for Barry Bonds' 73 home runs in 2001. The four 20-win rotation of the 19691971 Orioles is also counted here.
Not all the records are positive (where would the fun be in that?), and some are more interesting than others, but at least now no one can say that the Royals (or Nats or your-least-favorite-team-here) sucks at everything. All records were found using Baseball-Reference's Play Index.
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Arizona Diamondbacks: Most strikeouts, 223 (Mark Reynolds, 2009)
Atlanta Braves: Most consecutive games with at least one strikeout by the pitching staff, 2,326 (August 16, 1995 - today)
This is my favorite record on the list. The Braves have struck out a batter in every game since August of 1995. Tom Glavine started that game against Jeff Conine, Terry Pendleton, and Andre Dawson and the Marlins, but the young club was somehow able to escape without a single strikeout. It hasn't happened again.
Baltimore Orioles: Most pitchers with 20+ victories, 4 (19691971 O's - tied with 1920 White Sox)
Boston Red Sox: Lowest WHIP, 0.737 (Pedro Martinez, 2000)
Chicago Cubs: Most RBIs, 191 (Hack Wilson, 1930)
Chicago White Sox: Fewest baserunners allowed in 162 game season, 163 (Eddie Fisher, 1965)
Cincinnati Reds: Most players with 25+ saves, 2 (1990 Reds)
Besides the Marlins and Rays, I had the most trouble finding a record for the Reds. Considering how many all-time greats they've had on their teams, it still surprises me.
Cleveland Indians: Most GIDPs induced, 47 (Gaylord Perry, 1973)
Colorado Rockies: Most players with 40+ home runs, 3 (1996 Rockies - tied with 1973 Braves)
Detroit Tigers: Most players with 200+ hits, 4 (1937 Tigers - tied with 1929 Phillies)
Florida Marlins: see Tampa Bay Rays
Houston Astros: Most consecutive games with batter getting hit-by-pitch, 10 (July 7 - July 14, 2006)
Kansas City Royals: Most consecutive games with no batters striking out, 3 (July 17 - July 19, 1975)
Los Angeles Dodgers: Most sacrifice flies by batter, 19 (Gil Hodges, 1954)
Los Angeles Angels: Most strikeouts by pitcher, 383 (Nolan Ryan, 1973)
Milwaukee Brewers: Most batters with 150+ strikeouts, 3 (2001 Brewers)
Minnesota Twins: Fewest walks allowed in a full season, 9 (Carlos Silva, 2005)
New York Mets: Fewest hits allowed in a full season, 108 (Sid Fernandez, 1985)
This seems like a record people would know about. I wonder what his BABIP was that year...
New York Yankees: Total bases, 457 (Babe Ruth, 1921)
So many records that could've gone here...
Oakland Athletics: Most stolen bases, 130 (Rickey Henderson, 1982)
Philadelphia Phillies: Most shutouts by a pitcher, 16 (Pete Alexander, 1916)
Pittsburgh Pirates: Most triples, 36 (Chief Wilson, 1912)
San Diego Padres: Most pitchers with at least one victory, 24 (2009 Padres)
San Francisco Giants: Most home runs, 73 (Barry Bonds, 2001)
Seattle Mariners: Most hits by a batter, 262 (Ichiro!, 2004)
St. Louis Cardinals: Highest average game score, 78 (Bob Gibson, 1968)
Tampa Bay Rays: Most batters with 100+ strikeouts, 6 (2006 Devil Rays - tied w/2006-08 Marlins, 2008 Brewers)
You may notice that this record is eerily close to the Brewers record above. It was the only thing I could find that had the Rays and/or Marlins on the top, though. If someone can find something more interesting and/or unique, I'd be happy to have it.
Texas Rangers: Most doubles allowed, 68 (Rick Helling, 2001)
It seemed like the Rangers kept finding their way to the top of these "Most X allowed by a pitcher" lists. This doubles number was the most interesting.
Toronto Blue Jays: Most pickoffs by a pitcher, 23 (Jerry Garvin, 1977)
Washington Nationals: Most hit-by-pitch by a batter, 50 (Ron Hunt, 1971 Expos)
I suspect that not everyone will agree with my putting a Montreal record here, but the Nationals have been around for so few years that I don't really have a choice.
So there you have it. What other records might I have missed?