Here's how the Twins acquired each of the members of the 25 man roster. Each player is traced back as far as possible in the organization.
Pitchers
Luis Ayala: Signed as a free agent on February 6, 2009.
Scott Baker: Drafted in the 2nd round of the 2003 amateur draft.
Nick Blackburn: Drafted in the 29th round of the 2001 amateur draft.
R.A. Dickey: Signed as a free agent on December 26, 2008.
Matt Guerrier: Selected off of waivers from the Pittsburgh Pirates on November 20, 2003.
Sean Henn: Signed as a free agent on December 16, 2008.
Francisco Liriano: Traded by the San Francisco Giants with Boof Bonser and Joe Nathan for A.J. Pierzynski and cash. A.J. Pierzynski was drafted by the Twins in the 3rd Round of the 1994 amateur draft.
Jose Mijares: Signed as an amateur free agent on March 2, 2002.
Joe Nathan: Traded by the San Francisco Giants with Boof Bonser and Francisco Liriano for A.J. Pierzynski and cash. A.J. Pierzynski was drafted by the Twins in the 3rd Round of the 1994 amateur draft.
Glen Perkins: Drafted in the 1st round of the 2004 amateur draft.
Kevin Slowey: Drafted in the 2nd round of the 2005 amateur draft.
Summary of the pitchers. Four were drafted, two were traded for, three were signed as free agents, one was signed as an amateur free agent, and one was claimed off of waivers.
Catchers
Joe Mauer: Drafted 1st overall in the 2001 draft. (Mark Prior!!!!!!!!)
Jose Morales: Drafted in the 3rd round of the 2001 draft. (Two catchers in the first three rounds with A.J. on the major league roster!)
Mike Redmond: Signed as a free agent on November 24, 2004.
Summary of the catchers: Two were drafted in the same draft and one was signed as a free agent.
Infielders
Brian Buscher: Drafted from the San Fransisco in the 2006 Rule 5 draft. I believe this was the minor league Rule 5 draft.
Joe Crede: Signed as a free agent on February 21, 2009.
Brendan Harris: Traded by the Tampa Bay Rays with Delmon Young and Jason Pridie for Eduardo Morlan, Jason Bartlett and Matt Garza. Morlan was drafted in the 3rd round in the 2004 draft. Bartlett was traded by the San Diego Padres to the Minnesota Twins for Brian Buchanan. Buchanan was traded by the New York Yankees with Cristian Guzman, Eric Milton, Danny Mota, and cash for Chuck Knoblauch. Knoblauch was drafted in the 1st round of the 1989 draft. Garza was drafted in the 1st round of the 2005 draft.
Justin Morneau: Drafted in the 3rd round of the 1999 draft.
Nick Punto: Traded by the Philadelphia Phillies with Carlos Silva and Bobby Korecky for Eric Milton. Milton was traded by the New York Yankees with Cristian Guzman, Brian Buchanan, Danny Mota, and cash for Chuck Knoblauch. Knoblauch was drafted in the 1st round of the 1989 draft. Note: Punto was originally drafted by the Twins in 1997 in the 33rd round but did not sign.
Matt Tolbert: Drafted in the 16th round of the 2004 draft.
Summary of the infielders: Two were drafted, two were traded for, one was signed as a free agent and one was drafted in the Rule 5 draft.
Outfielders
Michael Cuddyer: Drafted in the 1st round of the 1997 draft.
Carlos Gomez: Traded by the New York Mets with Deolis Guerra, Kevin Mulvey, and Philip Humber for Johan Santana. Santana was traded by the Florida Marlins for Jared Camp. Note: Santana was a Rule 5 draft out of the Houston Astros organization, and thus, the Twins were required to keep him on the 25 man roster during the entire 2000 season.
Jason Pridie: Traded by the Tampa Bay Rays with Delmon Young and Jason Pridie for Eduardo Morlan, Jason Bartlett and Matt Garza. Morlan was drafted in the 3rd round in the 2004 draft. Bartlett was traded by the San Diego Padres to the Minnesota Twins for Brian Buchanan. Buchanan was traded by the New York Yankees with Cristian Guzman, Eric Milton, Danny Mota, and cash for Chuck Knoblauch. Knoblauch was drafted in the 1st round of the 1989 draft. Garza was drafted in the 1st round of the 2005 draft.
Delmon Young: Traded by the Tampa Bay Rays with Brendan Harris and Jason Pridie for Eduardo Morlan, Jason Bartlett and Matt Garza. Morlan was drafted in the 3rd round in the 2004 draft. Bartlett was traded by the San Diego Padres to the Minnesota Twins for Brian Buchanan. Buchanan was traded by the New York Yankees with Cristian Guzman, Eric Milton, Danny Mota, and cash for Chuck Knoblauch. Knoblauch was drafted in the 1st round of the 1989 draft. Garza was drafted in the 1st round of the 2005 draft.
Summary of the outfielders: One was drafted, three were traded for.
Designated Hitter
Jason Kubel: Drafted in the 12th round of the 2000 draft.

I love these sorts of things. Thanks, Boss.
Seconded. Thanks.
The thought of _elm_n Young as an infielder makes me cringe. But I'm with bS, well done.
We signed Ayala in 1999?! Also, your outfielders heading says "infielders."
Otherwise, I too love stuff like this.
Amazing how Buck F'n Buchanan was all it took to get Jason Bartlett, and the Twins still came up way behind on him.
Amazing how Buck F'n Buchanan was all it took to get Jason Bartlett, and the Twins still came up way behind on him.
tru dat.
Good stuff. Interesting to see the churn of players.
Although I know this is what actually happened, feels disingenuous to refer to an extortion move as a trade.
I should have noted originally that Santana was a Rule 5 pick and therefore needed to stay on the major league roster. I've added that now.
Half baked crap, I tell ya! I fixed the errors pointed out.
I hate to say it, Boss, but I now notice that under Joe Nathan's entry, Francisco Liriano is referred to as A.J. Pierzynski.
Note to self: write the post and then drink the ten beers. Order is important.
Note: Santana was a Rule 5 draft out of the Houston Astros organization, and thus, the Twins were required to keep him on the 25 man roster during the entire 2000 season.
Now that I think about it, Santana's suckage in 2000 helped us get Mauer in 2001, which of course helped him when he got to pitch to Mauer. Quite a devious ploy by Santana when you think about it. (Also, it's sad that AG doesn't sponsor Johan's bb-ref page any more and now it is sponsored by some 11-year-old Phillies fan whose sole purpose is to mock the Mets.)
I believe this was the minor league Rule 5 draft.
Yup, Buscher was in the AAA phase of the Rule 5 draft, so the Twins only needed to ensure that he stayed at the AAA level that year.
Yup, Buscher was in the AAA phase of the Rule 5 draft, so the Twins only needed to ensure that he stayed at the AAA level that year.
I don't think that's actually how the minor-league phase of the Rule 5 works, is it? Buscher played two-thirds of his first year with the Twins in Double-A.
Weird--I don't quite understand the point of the minor league Rule 5 if you can keep a prospect mired at the same level, but that is indeed what happened.
In all fairness to AJ, I don't think the Twins drafted two high-pick catchers in 2001; wasn't Morales an IF that was converted to catcher? Not that we really need to be fair to AJ...