The Rams missed on draft picks far more often than not during their time in St. Louis. Even if only by luck, they had a handful of outstanding picks. Let's take a look at the draft selections that just missed making the list.
Grant Wistrom (1998, 1st Round - 6th Overall)
Wistrom had a very solid career with the Rams. I like to think of him as a poor man's Chris Long. He was a very high energy player who was dependable - if unspectacular. He played his first 6 seasons with the Rams before bolting for greener pastures as a free agent in 2004. His defection to the Seahawks stoked the fire of the STL-SEA rivalry of the early 2000s.
Ryan Fitzpatrick (2005, 7th Round - 250th Overall)
Fitzpatrick has bounced around the NFL since being drafted by the Rams, but has proven to be a dependable backup and short term solution for several franchises. If he would have stuck with the Rams and had his same success, he likely would have made the top 10.
O.J. Atogwe (2005, 3rd Round - 66th Overall)
Atogwe was a tremendous steal in the 2005 draft. He was the toughest individual to leave off of the list. After he became a starter in 2006, he turned into a turnover machine - accumulating 37 interceptions and forced fumbles. He was one of the best players on the Rams during that stretch before bolting to the Redskins on a huge free agent deal.