It's fun to think that every pick will be a starter or even contribute, but it doesn't work out that way. Keep in mind here: the Rams had very high picks during many of these drafts and multiple picks. Plus they were a god awful team so some of the scrubs actually played and/or started but were out of the league after they left the Rams.
Many were released or traded away after the Rams released they were not very good: e.g., T Austin, Cooper.
2016 1 Jared Goff
2016 4 Tyler Higbee
2016 4 Pharoh Cooper
2016 6 Temarrick Hemingway
2016 6 Josh Forrest
2016 6 Mike Thomas
2015 1 Todd Gurley
2015 2 Rob Havenstein
2015 3 Jamon Brown
2015 3 Sean Mannion
2015 4 Andrew Donnal
2015 6 Bud Sasser
2015 6 Cody Wichmann
2015 7 Bryce Hager
2015 7 Martin Ifedi
2014 1 Greg Robinson
2014 1 Aaron Donald 13
2014 2 Lamarcus Joyner
2014 3 Tre Mason
2014 4 Maurice Alexander
2014 6 E.J. Gaines
2014 6 Garrett Gilbert
2014 7 Mitchell Van Dyk
2014 7 C.B. Bryant
2014 7 Michael Sam
2014 7 Demetrius Rhaney
2013 1 Tavon Austin
2013 1 Alec Ogletree
2013 3 T.J. McDonald
2013 3 Stedman Bailey
2013 4 Barrett Jones
2013 5 Brandon McGee
2013 5 Zac Stacy
2012 1 Michael Brockers
2012 2 Brian Quick
2012 2 Janoris Jenkins 39
2012 2 Isaiah Pead
2012 3 Trumaine Johnson
2012 4 Chris Givens
2012 5 Rokevious Watkins
2012 6 Greg Zuerlein
2012 7 Aaron Brown 209
RIP Bucky - 7/25/1943 - 1/19/2013