As a quick follow-up to my previous post: I did a search for the teams since 1950 with the fewest All-Stars at any point in their career. Obviously, every team has at least one All-Star since each team gets one representative. Only one team has had as few as two career All-Stars: the 2011 Kansas City Royals (Joakim Soria and Aaron Crow). Of course, that's misleading; many 2011 Royals were just beginning their careers and hopefully more than a few will eventually become All-Stars.
Most of the teams near the bottom of the list are either recent teams (2011 Blue Jays, 2011 Astros, 2010 A's) or early seasons of expansion franchises (1969 Royals, 1971-'72 Padres, '77 Mariners). Looking at mature franchises, here are a few that jump out at me.
1977-'78 Minnesota Twins: The '77 Twins had just five career All-Stars (Rod Carew, Larry Hisle, Butch Wynegar, Roy Smalley and Tom Burgmeier), despite which it won 84 games with Carew winning the MVP Award. It had some good players like outfielders Lyman Bostock and Dan Ford, plus 20-game winner Dave Goltz. The '78 Twins had just four All-Stars -- Carew, Wynegar, Smalley and reliever Mike Marshall. The team finished 73-89, although it was outscored by just 16 runs and actually led the American League in on-base percentage. Goltz and Geoff Zahn finished in the top 10 in the league in ERA and Marshall was a good closer. The rest of the staff was nondescript and the team had no power, but I don't think this was the least talented team ever assembled.
2004 Montreal Expos: A good candidate with just five career All-Stars and not exactly a murderer's row of stars at that: Livan Hernandez, Tony Batista, Jose Vidro, Chad Cordero and Carl Everett. In their final year in Montreal, the Expos lost 95 games, drew under 800,000 fans and ran through 46 different players. They had some interesting players, however: Orlando Cabrera, Nick Johnson, the other Alex Gonzalez. Hernandez was the only pitcher to start 20 games, but the team wasn't at the bottom of the league in either runs scored or runs allowed.
1950 St. Louis Browns: A terrible team (58-96) with five career All-Stars: Sherm Lollar, Roy Sievers, Ned Garver, Frankie Gustine and Snuffy Stirnweiss. Lollar was a good catcher, later traded to the White Sox, made the All-Star team seven times in the '50s and twice finished ninth in the MVP vote. Sievers had a fascinating career that I won't recount here, but he hit 318 career home runs. Another interesting playing was a small outfielder named Dick Kokos. He'd played well in 1949 and 1950 at ages 21 and 22 (.261, 41 home runs, .363 OBP) but was drafted into the military in 1951, lost two seasons, and didn't play well when he returned. A strong contender.
2003 Detroit Tigers: This is the team that lost 119 games; it had six players who were All-Stars at some point in their careers: Steve Avery, Omar Infante, Brandon Inge, Dean Palmer, Carlos Pena and Dmitri Young. Avery was at the end of the line and the only other two other pitchers of note were 20-year-old rookie Jeremy Bonderman and 21-game loser Mike Maroth, who did manage to win 50 games in his career. My favorite stat from this team: Nate Cornejo started 32 games ... and struck out 46 batters. He had nine starts in which he didn't strike out a single batter.
Anyway, there's a more thorough way to examine this topic as well, although simply examining the worst teams is probably a good start.