I don't remember the Blizzard of '78. The two that I remember were Hurricane Gloria in 1985, and the July 10, 1989 tornado outbreak.
I remember
both Blizzards of '78 (January 20, and the much more infamous one), as well as an ice storm in between the two. For hurricanes my memories include Belle (1976), Gloria (1985), and Bob (1991) on Long Island, and three of the four big Florida hurricanes of 2004, as well as Hurricane Irma last year. For some crazy reason, I don't remember Hurricane Agnes or the Ice Storm of 1973, and I would've remembered something like that.
I do remember the 1974 Super Outbreak. Not because it gave Long Island any tornadoes, but because we got the tail end of it... that and I saw footage of it on the news. Evidently that storm brought us thunderstorms that were so severe, that it took me a little longer to get over my childhood fear of thunder, which I found embarrassing at the age of eight.
The Buffalo Blizzard of '77 , which I also only saw on the news, was also part of a severe winter that brought snow to the tri-state area, and even into Florida. This was the first time in my life I saw snow as a threat. Even the "Lindsay Snowstorm" of '69 didn't do that for me.
After '78, the only blizzards for me were the Yankee Opening Day Blizzard of '82, the March Blizzard of '83, the "Storm of the Century" in '93, the big blizzard of '96, a long forgotten one from December 2005, and Winter Storm Stella from last March.
One other storm that brought tornadoes to the Berkshires in Massachusetts in the 1990's had a lesser impact on Long Island. I actually remember I was out at a shopping center in Farmingville, and one of the signs to a laundromat was flapping around in the wind, while still sticking to the frame on the building. I had my old Toyota Van at the time, and I offered to catch the thing before it could break loose, and they begged me to do it. I stood on the rear bumper of my van, where I managed to catch one corner, then I caught the other and it landed on my head. I brought it down and gave it to the manager who told me their landlord was taking too long to get them a new sign. They gave me something for free, but I can't remember what it was. Maybe a cup of coffee or something like that.
Beyond that, there have been storms on Long Island and in Florida that I've been through which spawned tornadoes, but I've never had any encounters with those tornadoes.
And I'm sure I'm forgetting others.