Yet there also have been a few key departures of those special talents who were drafted or signed and then developed into stars by one organization, notably Albert Pujols leaving the Cardinals behind two winters ago.
In recent years, nobody has ridden one-team wonders longer than the Yanks, but the Phillies come close, with a trio of their own among players beyond or approaching 10 seasons with the club. Appropriately, the Twins have a pair of those.
Here's a list of the longest-tenured one-team players in the Majors, based on their debut date:
Mariano Rivera, Yankees
Debut: May 23, 1995
All he has done since arriving in the Majors is become the all-time saves leader and one of the most celebrated postseason performers ever. The Yanks went more than a year before this week without having both Rivera and Jeter in uniform, thanks to a pair of devastating injuries. At 43, Rivera is the game's elder statesman in his farewell season.
Derek Jeter, Yankees
Debut: May 29, 1995
With his delayed 2013 debut in the books, Jeter got back to business in a Hall of Fame career that has no expiration date just yet, other than the 2014 player option he holds. If he can stay healthy, Jeter has a chance to finish his career well into the top 10 in both hits and runs.
Todd Helton, Rockies
Debut: July 1, 1995
Along with Jeter, Helton was one of the first to get the type of contract that etches in stone a player's status as a one-team wonder. The Rockies first baseman signed a nine-year extension in 2001 that took him through 2011, and he's in the second year of a subsequent two-year deal at age 40. For now, Helton is far and away the franchise leader in hits, homers, RBIs, runs and most every other offensive category -- at least until Tulowitzki gets there.
Jimmy Rollins, Phillies
Debut: Sept. 17, 2000
One of the Phils' vaunted trio of homegrown stars that led the team to back-to-back World Series appearances, including the title in 2008, Rollins might be making more Philadelphia history than you'd think. Only Mike Schmidt has played more games in a Phillies uniform than Rollins, and he's only about 100 hits behind Schmidt.
Brian Roberts, Orioles
Debut: June 14, 2001
Long the centerpiece of the team, Roberts has struggled mightily with injury the last three-plus seasons, topping out with 59 games played during that time span. He's back on the field with the O's as of last month, hoping to be a part of the type of run he missed out on a year ago.
Chase Utley, Phillies
Debut: April 4, 2003
If you listen to the trade rumors, this is one guy who might not be a one-team wonder for much longer. Utley's name has been bandied about as the Trade Deadline approaches, largely because he won't have earned 10-and-5 full no-trade rights until August and is a free agent at the end of the year.
Justin Morneau, Twins
Debut: June 10, 2003
Another franchise lifer who has seen his career marred by injury, Morneau won the American League MVP Award in 2006 for the Twins, joining an eclectic list of Minny MVPs that (at the time) included Rod Carew, Harmon Killebrew and Zoilo Versalles. More than ever, Morneau's status with the Twins is up in the air -- he's a free agent at season's end and some teams reportedly are making inquiries.
Joe Mauer, Twins
Debut: April 5, 2004
Mauer added his name to the list of MVPs for his hometown team in 2009, and he signed an eight-year, $184 million deal that next offseason. Health, again, has been an issue, but Mauer's back in All-Star form the last couple of seasons and at age 30 looks back on track.
Yadier Molina, Cardinals
Debut: June 3, 2004
His reputation upon reaching the Majors was that he would be the most talented of the Molina brothers, which was saying quite a lot since Bengie and Jose already had established the name as the first family of catching. But Yadi has been all that and more, becoming a stalwart in a post-Pujols era of success in St. Louis. He's wrapped up through 2017 with a mutual option, and for that franchise No. 4's career might ultimately play out more like No. 6's than No. 5's.
David Wright, Mets
Debut: July 21, 2004
Cue the biggest ovation at introductions for the 2013 All-Star Game. Wright has been a model Met since arriving on the scene, and he'll be starting at third base at Citi Field next Tuesday. Last winter, he signed a deal that will keep him with the Mets through 2020, when he'll be in his age-37 season.
Ryan Howard, Phillies
Debut: Sept. 1, 2004
The third of the trio of All-Stars that have been so productive for the Phils, followed by Cole Hamels and Carlos Ruiz as homegrown veterans, Howard too has been hit hard by health issues in recent years, now on the DL after knee surgery that will knock him out six-eight weeks. At age 33, he's signed through 2016, with a club option at $23 million for '17.
This winter, the historic allure of the pinstripes will be tested again, as second baseman Robinson Cano (May 3, 2005) plays out his final year before free agency. Others such as the Tigers' Justin Verlander (July 4, 2005), the Mariners' Felix Hernandez (Aug. 4, 2005), the Giants' Matt Cain (Aug. 29, 2005) and the Nationals' Ryan Zimmerman (Sept. 1, 2005) have deep histories already with their original clubs and long-term deals taking them well into their 30s.
As their time racks up, other one-team wonders will emerge from a pool of players in their late 20s who have established themselves in the Majors with their one and only club.
But they have a long way to go to match the likes of Jeter and Rivera, or for that matter Molina, Wright and Howard.
Being a one-team man takes time, talent and a mutual appreciation, and those things are hard to find all in one place. That's why one-team wonders will always be something to cherish, no matter how many of them there are.