This one is easy to decide, so I'm going to skip the whole nominee part. Grady Little entered into consideration for half a second, but this guy is the biggest goat in recent Boston sports history...
Manny Ramirez, formerly of the Boston Red Sox.
We tend to forget recent Red Sox history before 2003. But I remember how much criticism Manny Ramirez took. Remember when he was "sick" and was then caught having drinks with Enrique Wilson? Remember when he slid hands-first into home and broke his fingers? Remember all the fly-balls he walked out, all the questionable injuries, all the defensive miscues.
Then through '04-'07, we fell back in love with him. It was sort of like a shaky marriage that had suddenly won the lottery. The problems were still there, but the joy of winning overwhelmed and minimized those problems.
Then he pushed down a Sox employee for not having enough tickets for him. Then he slapped a teammate IN PUBLIC. Finally, he was sent packing after giving the Sox an ultimatum.
Manny won the Goat of the Year Award twice, and this is only the 4th year I've been doing this.
Oh yeah, he also took PEDs.