According to a recent article by John Clayton (ESPN link), here are the ten top-spending clubs in free agency. This list includes only unrestricted free agents, so the Bengals are not on this list since they signed very few UFA's from other teams.
#1 Miami Dolphins: 8 players, $146.1 million
#2 Indianapolis Colts: 8 players, $132 million
#3 Tennessee Titans: 10 players, $97.2 million
#4 Philadelphia Eagles: 10 players, $95.6 million
#5 Cleveland Browns: 8 players, $87.1 million
#6 St. Louis Rams: 2 players, $69.1 million
#7 Kansas City Chiefs: 8 players, $62.4 million
#8 Chicago Bears: 7 players, $60 million
#9 Tampa Bay Buccaneers: 7 players, $50.4 million
#10 Detroit Lions: 3 players, $49 million
If you include all the free agent contracts for players eligible to change teams (i.e. no EFA or RFA deals included since they are locked into the Bengals in some form) the team total would have been 18 players, $94.2 million. As you can see, although the total dollar amount looks like top ten material, the fact that this is for 18 players shows that the team actually spent very little so far.
If MJ93 is able to work out a long-term deal and/or extensions can be negotiated with Atkins, Dunlap, etc. this will change by quite a bit. Two of these players combined could easily surpass the entire total committed thus far.