Miss Piggy never appeared on Sesame Street. She never appeared in a background shot, either. It's one of those "urban legends" that's popped up over time, but chalk it up to faulty memories and vivid imaginations.
No one who says they've seen her on there is able to produce any clips or photos that prove it.
For copyright reasons, none of the characters from TMS were allowed to cross over onto SS (except for Kermit, since he appeared on SS long before TMS). Even when they did, they usually had to build a new puppet and create a new name for it. See the "Mahna Mahna / Bip Boppadatta" thread in the Sesame section of this forum for more details.
I believe that the Beautiful Day Monster (a generic name) was even a slightly different puppet on SS than in TMS.
It's worth noting that while Rowlf, a TMS character, did appear in the "Nine" sketch, he was already created prior to TMS. He was on The Jimmy Dean Show in the early 60's, and the appearance on SS (only one appearance, in the first episode from 1969) had nothing to do with TMS, as that show didn't premiere until 1976.
(Hmm. So how was Rowlf able to appear and Mahna Mahna wasn't? Sorry, I don't know. I'm going off of the info that the lady from Henson sent us in the Mahna Mahna thread.)
It's ironic that the SS Muppets were able to make so many appearances on TMS, but not the other way around. In addition to Big Bird showing up on the Leslie Uggams episode, and several of the characters showing up in the Muppet movies (as already mentioned), Bert and Ernie show up in the Connie Stevens episode. (They also put in a cameo in the "Valentine" special that was one of the original pilots for the series.) Also, there are the crossovers in Muppets: A Celebration of 30 Years and Muppet Family Christmas.
So why did the Sesame folk come over so much, but not the other way around? Dunno. I'm guessing that, at the time, Jim and co. were looking to distance TMS as much from pre-schooler fare as possible. And while it was deemed classy for characters from Henson's previous hit series to appear to boost the ratings on TMS, having the TMS characters appear on Sesame would "kiddify" them too much. (Or so they feared, it seems, until the debut of the Muppet Babies.)
The TMS Muppets could certainly make an appearance now, but the problem is that the characters aren't well known enough among the mass audience. It wouldn't be a cool celebrity cameo, because the TMS Muppets aren't big enough celebrities right now. Maybe after the Muppets' star has been built up a little more, this long-awaited crossover can happen.
Hope that helped.
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