I've always had a fascination with sports trivia and out of curiosity I looked up the professional sports teams which hold the record for the most consecutive losing seasons for their respective sport. Here is what I found:
MLB
Pittsburgh Pirates 18 losing seasons in a row
NFL
Tampa Bay Buccaneers 14 losing seasons in a row
NHL
Couldn't find this data. Maybe one of our Canadian SimHQ members knows this one?
NBA
Sacramento Kings 16 losing seasons in a row