Why they would sign him: Along with the Arizona Cardinals, the Colts unsuccessfully tried to claim running back Ben Tate off waivers; he was awarded to the Minnesota Vikings after being cut by the Cleveland Browns. The Colts lost running back Ahmad Bradshaw to a season-ending injury, and Trent Richardson hasn't lived up to expectations since being acquired in a trade last year. Colts coach Chuck Pagano was the Ravens' defensive coordinator during Rice's tenure in Baltimore.
Why they won't sign him: The Colts probably aren't inclined to add a controversial player given that their owner, Jim Irsay, has a history of substance-abuse issues, including a six-game suspension for pleading guilty to a misdemeanor count of operating a vehicle while intoxicated. The Colts already have a prolific offense, even without a proven running back.
New England Patriots
Why they would sign him: The Patriots lost Stevan Ridley for the season and have some depth concerns. Patriots coach Bill Belichick also has shown a willingness to take on controversial players who have had trouble with the law, including Corey Dillon, Aaron Hernandez and Randy Moss. Belichick is also good friends with Greg Schiano, Rice's coach at Rutgers, and has an affinity for former Scarlet Knights players.
Why they won't sign him: It would go against the stated wishes of owner Robert Kraft, who said publicly that Rice would not play for the Patriots. Kraft has taken a strong stance against domestic violence in the past, cutting former Nebraska defensive tackle Christian Peter when his extensive criminal history came to light soon after he was drafted. The Patriots recently bolstered their backfield by signing LeGarrette Blount to a two-year, incentive-laden contract. Former Ravens practice squad running back Jonas Gray excelled Nov. 17 against the Indianapolis Colts with 201 rushing yards and four touchdowns.
Why they would sign him: C.J. Spiller is hurt and out until at least late December, and Fred Jackson has been in and out of the lineup with injuries. The Bills are still contenders for a playoff berth, and having a running game to complement quarterback Kyle Orton could be the difference. Rice's Atlanta-based sports agency is owned by new Bills co-owner Terry Pegula.
Why they won't sign him: It's unknown whether the Bills could plug Rice into the lineup and get production out of him this late in the regular season. Bills coach Doug Marrone is regarded as a stern disciplinarian and might not want to bring in Rice.
Why they would sign him: The Cardinals have dealt with several injuries in their backfield this season, including to starter Andre Ellington. The Cardinals are in line for a top seed in the playoffs and could use another offense playmaker to help out new starting quarterback Drew Stanton.
Why they won't sign him: It's highly unlikely that the Cardinals will want to deal with another public-relations crisis. Already this season, they dealt with a domestic-violence incident in which running back Jonathan Dwyer was charged with assaulting his wife.
Why they would sign him: The Cowboys could use an accomplished running back like Rice to help relieve workhorse DeMarco Murray, the NFL's leading rusher. With the Cowboys having their best season in years, Rice could give them an edge in the postseason with his versatility and ability as a receiver.
Why they won't sign him: Owner Jerry Jones is no stranger to controversy, but acquiring Rice might not be palatable. Safety C.J. Spillman is under investigation for an alleged sexual assault in September and was accused of attempted rape in December.
Why they would sign him: The Broncos rank 27th in the NFL in rushing offense and have been dealing with injuries to Montee Ball and Ronnie Hillman. Rice could give them a late-season boost in the ultra-competitive AFC West. The Broncos recently met with similarly controversial guard Richie Incognito but chose not to sign him immediately.
Why they won't sign him: Former undrafted free agent C.J. Anderson is a talented young player. Plus, Ball and Hillman are expected to return before the end of the regular season.
Why they would sign him: Knowshon Moreno is out for the season with a torn anterior cruciate ligament. They could use a running back for the future.
Why they won't sign him: Lamar Miller has had a solid season, proving capable of handling the lion's share of the carries. He has rushed for 614 yards and five touchdowns and is averaging 4.9 yards per carry. The Dolphins endured plenty of bad publicity a year ago during the bullying scandal involving Incognito and Jonathan Martin.