What NFL teams have been 11-0?

Answer 1

In 2009 season Colts and Saints.
Also, the 2007 Patriots (finished 16-0, but lost the Superbowl)
1998 Broncos (started 12-0, won the superbowl)
1972 Dolphins (14-0, won Superbowl)
1936 Bears (went 13-0 before losing to Giants in NFL's championship game.)

Those are 6 of the 14 teams to start a season 11-0.

***UPDATE***

These other teams went at least 11-0

2005 Colts (13-0, lost to Steelers in Divisional playoffs)
1985 Bears (12-0, won Super Bowl)
1991 Redskins (11-0, won Super Bowl)
1984 Dolphins (11-0, lost to 49ers in Super Bowl)
1969 Rams (11-0, lost to Vikings in Divisional Playoffs)

Now we have 11 of the 14 teams.

Answer 2

The Miami Dolphins are the only team that has went 14-0 and won the superbowl the same year, there are more games in a regular season now and the New England Patriots went 16-0 and lost the superbowl.