Per Eric Stephen from Dodger Thoughts. I didn't want this to get buried so he said I could post it here.
Inspired by a recent organizational chart someone made for the A's (I can't find the link to it), here is a history of how the current Dodger roster came to be (which is probably only interesting to me):
1987
1 & 2) Signed Pedro Astacio as an amateur FA (Dominican Republic)
>> traded to Colorado in 1997 for Eric Young
>> who was traded to the Cubs with Ismael Valdez in 1999 for Terry Adams, Brian Stephenson, and Chad Ricketts
>> Ricketts was traded with Luke Prokopec to Toronto in 2001 for Cesar Izturis and Paul Quantrill
>> Quantrill signed as a Type A FA with the Yankees in 2004; as compensation the Dodgers selected Blake DeWitt (round 1) and Justin Orenduff (sandwich pick)
1988
3) Signed Raul Mondesi as an amateur FA (Dominican Republic), June 6
>> traded with Pedro Borbon (see below) to Toronto in 1999 for Shawn Green and Jorge Nunez
>>Nunez was traded with Matt Herges (see below) to Montreal in 2002 for Wilkin Ruan and Guillermo Mota
>>Mota was traded with Paul LoDuca (see below) and Juan Encarnacion (see below) to Florida in 2004 for Hee Seop Choi, Billy Murphy, and Brad Penny
1991
1 & 2) Signed Ismael Valdez as an amateur FA - Mexico (see Astacio for the link to DeWitt & Orenduff)
1992
3) Signed Matt Herges as an undrafted FA (see Mondesi above for the link to Penny)
1993
3) Drafted Paul LoDuca, round 25 (see Mondesi above for the link to Penny)
1994
4) Signed Chan Ho Park as an amateur FA (South Korea)
>> Park signed with Texas in 2002 as a Type A FA; resulting compensation sandwich pick was Greg Miller
1996
5) Signed Luke Allen as an undrafted FA
>>was traded to Colorado in 2003 for Jason Romano
>>who was traded to Tampa Bay in 2004 for Antonio Perez
>>who was traded with Milton Bradley (see below) to Oakland in 2006 for Andre Ethier
1998
6) Signed Kevin Brown as a FA, December 12
>>traded for Jeff Weaver, Brandon Weeden, Yhency Brazoban, and cash in 2003
3) Signed Pedro Borbon as a FA, December 30 (see Mondesi link above)
1999
7) Drafted Jason Repko, round 1
8) Signed Hong-Chih Kuo as an amateur FA (Taiwan), June 19
2000
9) Signed Willy Aybar as an amateur FA (Dominican Republic), January 31
>>traded with Danys Baez (see below) to Atlanta in 2006 for Wilson Betemit
>>Betemit was traded in 2007 to the Yankees for Scott Proctor
3) Drafted Travis Ezi, round 12
>>traded to Florida in 2003 for Juan Encarnacion (see Mondesi above for link to Penny)
5) Signed Franklin Gutierrez as an amateur FA (Venezuela), November 18
>>who was traded to Cleveland in 2004 for Milton Bradley (see above for link to Ethier)
2001
9) Drafted Edwin Jackson, round 6
>>traded with Chuck Tiffany (see below) to Tampa Bay in 2006 for Danys Baez (see above) and All-Star Lance Carter
2002
10) Drafted James Loney, round 1
11) Drafted Jonathan Broxton, round 2
12) Drafted Delwyn Young, round 4
13) Drafted James McDonald, round 11
14) Drafted Eric Stults, round 15
15) Drafted Russell Martin, round 17
16) Signed Ramon Troncoso as an amateur FA (Dominican Republic), June 20
17) Signed Mario Alvarez as an amateur FA (Dominican Republic)
18) Signed Tony Abreu as an amateur FA (Dominican Republic), October 17
2003
19) Signed Chin-Lung Hu as an amateur FA (Taiwan), January 31
20) Drafted Chad Billingsley, round 1
9) Drafted Chuck Tiffany (see above), round 2
21) Drafted Xavier Paul, round 4
22) Drafted Matt Kemp, round 6
23) Drafted Lucas May, round 8
24) Drafted Travis Denker, round 21
>>traded to SF in 2007 for Mark Sweeney
25) Drafted Andy LaRoche, round 39
26) Signed Juan Rivera as an undrafted FA, July 21
>>traded to Kansas City in 2008 for Angel Berroa
2004
27) Drafted Cory Wade, round 10
28) Signed Jeff Kent as a FA, December 15
2005
29) Signed Derek Lowe as a FA, January 11
30) Drafted Jonathan Meloan, round 5
31) Signed Rafael Furcal as a FA, December 19
32) Signed Nomar Garciaparra as a FA, December 19
2006
33) Signed Joe Beimel as a minor league FA, January 25
34) Signed Takashi Saito as a minor league FA, February 7
35) Drafted Clayton Kershaw, round 1
36) Signed Juan Pierre as a FA, November 22
37) Signed Jason Schmidt as a FA, December 8
2007
38) Signed Chan-Ho Park as a minor league FA, November 8
39) Signed Andruw Jones as a FA, December 6
40) Signed Danny Ardoin as a minor league FA, December 12
41) Signed Hiroki Kuroda as a FA, December 15
42) Signed Gary Bennett as a FA, December 17
2008
43) Signed Luis Maza as a minor league FA, February
In addition:
351 You forgot drafting Mike Piazza in '88 and signing Zeile in '97. Mike Piazza was then traded with Todd Zeile to the Marlins for Gary Sheffield, Bobby Bonilla, Charles Johnson, Jim Eisenreich, and Manuel Barrios in '98.
Sheffield was then traded to the Braves in 2002 for Odalis Perez, Brian Jordan, and Andrew Brown.
Andrew Brown was then sent with Franklin Gutierrez to the Indians in exchange for Milton Bradley in '04.
Finally, Milton Bradley was packaged with Antonio Perez and traded to the Oakland A's for Andre Ethier in '05.