I know not all of the games were played ON the Bruins, but here is a list of all the Bruin's draft picks in history and NHL games:
http://www.hockeydb.com/ihdb/draft/teams/dr00004919.html
1997 was the last time we had 4 players that hit 100 game plateau: Thornton (1st) - 1431, Samsonov (8th) - 888, Clymer (27th) - 438 , Laaksonen (191st) - 483
Since then, here are the only players with 100+ NHL games each draft:
1998: Jonathan Girard (48th) - 150, Andrew Raycroft (135th) - 280
1999: Nick Boynton (21st) - 605, Mikko Eloranta (247th) - 264
2000: Andy Hilbert (37th) - 307, Jarno Kultanen (174th) - 102
2001: Shaone Morrison (19th) - 480, Andrew Alberts (179th) - 459, Milan Jurcina (241) - 430
2002: No one played more than 100 games, Yan Stastny (259th) played 91
2003: Mark Stuart (21) - 659, Patrice Bergeron (45th) - 882, Nate Thompson (183) - 534, Honorable mention: Byron Bitz (107th overall) - 97 games
2004: David Krejci (63rd) - 688, Kris Versteeg (134th) - 604, Matt Hunwick (461) - 224th
2005: Vladimir Sobotka (106th overall) - 381 games, Honorable mention:Matt Lashoff (22nd) - 74
2006: Phil Kessel (5th) - 814, Milan Lucic (50th) - 712, Brad Marchand (71st) - 519
2007: No one. And no honorable mentions
2008: Joe Colborne (16th) - 286, Honorable mention: Michael Hutchinson (77th) - 92 games
2009: Jordan Caron (25th) - 157
2010: Tyler Seguin (2nd) - 491, Ryan Spooner (45th) - 200
2011: Dougie Hamilton (9th) - 325
2012: No one (yet) - 4 players played in at least 1 NHL game this season. Included in 5 that have played in the NHL or AHL this season
2013: No one (yet) - 2 players have played at least 1 NHL game this season, Included in the 3 that have played in the NHL or AHL this season.
2014: David Pastrnak (25th) - 155, 1 additional has played NHL games this season and in the AHL
2015: 1 playing in the NHL (Brandon Carlo), 2 others playing in the AHL .