Red Kelly had a hat-trick for Detroit on October 21st, 1954, in a 5-3 win over Boston. One was on the power-play, one at even strength, and one short-handed.
Bobby Orr had 10 hat-tricks: 7 in Boston Gah-den and 3 on the road. One of those road ones was the famous playoff game at the Montreal Forum (April 11th, 1971) when he scored three in a 5-2 Boston win (though they of course lost the series). A weird one is March 31st, 1973 at Maple Leaf Gardens -- Orr scored 3... and the Bruins lost 7-3!
Brad Park had three for NYR between 1971 and 1975. (Two were in the 1971-72 season, and both of those against Pittsburgh.)
Paul Coffey had 5 hat-tricks: 4 with Edmonton between 1982-83 and 1985-86, and just 1 thereafter, with Pittsburgh only a month or two after he started playing for them (early 1988). Four of Coffey's five hat-tricks were achieved on the road.
Reijo Ruotsalainen picked up a hattie on March 17th, 1982 in the Rangers 5-2 win over Cooperalls-era Philly. That was his rookie season! (By comparison, Orr and Coffey each didn't get a hat-trick until their 3rd seasons.)
Ian Turnbull, who played most of his career with the 70s'/early-80s' Maple Leafs, must have one of the weirdest hat-trick records of any defenceman in League history: He got two hat-tricks, one with Toronto and one late in his career with L.A. The strange part? He scored a total of 9 goals in these two games! He famously scored 5 in a game against Detroit on February 2nd, 1977. But who knew he scored 4 in a game against Vancouver on December 12th, 1981? He scored 11 goals in total that season for L.A., meaning he scored 27% of his season's goals in one game.
Larry Robinson had only one career hat-trick. You're thinking c. 1977? Nope. He did it in his 14th NHL season, on Dec.19th 1985, in a 5-4 win over Quebec at the Colisée.
Ray Bourque also had only one hat-trick -- during Boston's big 1982-83 season, in an 11-5 thrashing of Quebec, also at the Colisée. (Bizarrely, the score was actually 4-4 almost midway through the second period... then Boston scored 7 of the next 8 goals.)
Brian Leetch, also had only one -- in the playoffs, May 22nd, 1995. However, the Flyers won the game over NYR 4-3, and went on to sweep the series. (Leetch somehow went -2 despite his hat-trick on the night.)
Al MacInnis had three hatties -- one with Calgary and two with St.Louis. I'm surprised to see that all three occurred in the mid-90s (i.e., none between 1982 and 1991 when scoring in general was higher).