This seems to be a popular thread. Let's see if I could contribute...
When I was really wee, I used to find the Sesame Street News Flash title card a little unnerving, maybe cause of the black background and high-contrast colors and Jerry Nelson's announcer voice. (Since I was born in the late 80s, I usually saw the 1980-1991 version of the title card, like this...)
http://images.wikia.com/muppet/images/9/9d/Firstday1.jpg
But a funny skit was almost always bound to follow, giving me my very first glimpse of Kermit the Frog in my childhood, and Jim Henson's Kermit for that matter! Once there was an episode from maybe the 1980s or early 1990s that featured the old animated Y skit about the talking yak who goes beserk in the end (after being insulted by the narrator) and charges toward the screen, wrecking the camera. If that wasn't enough, on this particular episode, the Sesame Street News logo ZOOMED right up to the screen after the collision, instead of cutting to it or fading up to it. I always found it odd why it did that instead of zooming up. To this day, I am trying to remember what News Flash skit that was. (It was probably one from the 1980s.)
But these News Flashes always introduced me to a character I began to know and love... Kermit the Frog. And this was years before I began watching "The Muppet Show" during its Nick reruns!
I also found the Pyramid skit a little weird, but I always would up enjoying it in the end. I saw it on my "Best of Ernie and Bert" VHS.
I am also very grateful I never saw the Beautiful Day Monster or Fred the Dragon on the show (they were probably long gone by 1990). They probably would've given my nightmares for years! I heard a lot of people were frightened by these two "creeps."
Also, I heard people were also scared of Lord Chatterly, Vincent Twice, and the Big Bad Wolf (the blue version, like in my avatar). I think that's why they replaced the blue version of the wolf with the purple version around maybe 1987-1988.