Update (2020 Draft):
In 2020, the Minnesota Vikings had 15 picks, giving them the record for most picks since the draft was limited to 7 rounds. This also gave them the most picks since the 2002 realignment and the most picks since the draft became a 3-day event.
Update (2016 Draft):
In 2016, the Cleveland Browns had 14 picks, tying the 1997 Miami Dolphins for most picks since the draft was limited to 7 rounds. This also gave them the most picks since the 2002 realignment and the most picks since the draft became a 3-day event.
I went and looked at all of the draft picks broken down by team here. It looks like the 7-round format started in 1994, although I've been having some serious problems trying to confirm this. I looked through the number of picks each team had and found the following:
- The highest number of draft picks by any team since the 7-round format started was by the Miami Dolphins. They used 14 total picks in 1997.
- Since the league was realigned into 8 divisions split between two conferences in 2002, two teams have had 13 picks: the 2010 Philadelphia Eagles and the 2004 Tennessee Titans.
- The 2010 Eagles also have the highest number of picks since the draft became a 3-day event in 2010.
- The team slated to have the most draft picks in 2013 is the San Francisco 49ers with 11.
I also took this opportunity to see which teams had the fewest number of picks. The 1999 New Orleans Saints had one draft pick. Apparently, they traded all six of their draft picks to the Redskins in order to get RB Ricky Williams with the fifth overall pick.