Has there ever been a undefeated baseball team?

Yes, the 1972 Miami Dolphins went 17-0 and are the only team (so far) to go through the entire NFL regular season (14 games at the time) and postseason undefeated.

The 2007 New England Patriots also went undefeated in the regular season, going 16-0. They won their next two postseason games but lost in Super Bowl XLII to the New York Giants, ruining their undefeated season.

In number of consecutive wins, the Pats technically outdid the Dolphins by reeling off 18 straight victories (thanks to the longer, 16-game regular season), but their Super Bowl loss (to an arguably inferior team) permanently tarnished an otherwise incredible run.