The Ottawa Senators — their second incarnation, anyway — broke into the NHL in 1992 with an impressive 5-3 victory against Montreal. Then lost 20 of their next 21 games.
The 1972-73 New York Islanders entered the league alongside the Atlanta Flames, but quickly fell behind their expansion brethren, and stayed there. New York finished 12-60-6, good for 35 fewer points than Atlanta. [Never mind that the Islanders later would launch a run of four consecutive Cups a few months before the Flames relocated to Calgary.]
And then there were the 1974-75 Washington Capitals, who debuted with an 8-67-5 record.