Defeating the Undefeatable: Went undefeated for his whole first year in WWF, to play up his "Perfect" gimmick. The streak ended rather anticlimactically with mid-carder Brutus Beefcake beating him at Wrestlemania VI.
He had lost to Hulk Hogan at some house shows a few months earlier, but none of those were televised.
Jack of All Stats: Hennig used a combo of power moves, more agile attacks, and submission holds in his arsenal. In a meta-sense, Curt also had great psychology, variety of moves, promo skills, and a great general charisma about him.
Lightning Bruiser: Agility? He could hit missile dropkicks and jump over opponents. Strength? Once Perfect-Plexed The Big Show. Endurance? Could wrestle for long periods of time and put on great matches even with real injuries. (He wrestled through his Summerslam classic against Bret Hart with a back problem)
Loveable Rogue: In a time when nobody rooted for the bad guy, he was the asshole heel who was secretly admired by many fans. It's why his Face-Heel Turn was more seamless than others.
Theatrics Of Pain: He had the ability to make his opponents look much better than they were. This was probably why he was used more to put lesser talents over rather than being a Main Eventer.
To be more specific, he was well-known for twirling in mid-air while taking powerful strikes (such as a clothesline). He also had his own variation of the "Flair Flip" that he would work into most matches, especially before his back injury.
Trickster Archetype: In Real Life, Curt loved to prank people not unlike Owen Hart. Once he went to a party and crapped in the hosts' baby's potty and managed to convince them their kid took an adult-sized shit.
Vitriolic Best Buds: After turning face he had this relationship with old adversary Bret Hart. They teamed together quite often, and bickered about who was better just as often.
Wrestling Family: Curt was the son of Larry "The Axe" Hennig and now his own son Joe wrestles in WWE as Curtis Axel (formerly Michael McGillicutty of The Nexus). His daughter, Amy, is also a wrestler.