Also found on ebay, offered July 2002 for 25$
"...to promote the video game back in the 80's, nintendo made winter hats for the ultra popular game mike tysons punch out. This product is an official piece of nintendo history. It has been mine since i was 5. i dont even remember getting it. but it is still in great condition. it is a normal size beanie winter cap. it is red white and black. it says nintendo and has a punch out logo on the brim. the punch out logo is made of soft plastic/velvet. this hat is extremely rare and is an awesome piece of history... get this quick, because this is no joke. try to find this again on ebay! i dare you! The first picture shows the front of the hat, the second shows the back. it says nintendo twice as it wraps around the entire hat. the brim is about 9" when laid down, and from top to bottom is 8.5". it is a stretchy cap though, so one size is guarenteed to fit all..."

Latest news:
I got mail by someone informing me that there are more of those beanie caps out there. He says that he has got the Zelda 1 beanie:
"...I remember those beanies! ...as a matter of fact, i found my Legend of Zelda beanie just last month!! ... its the same style as your Punch out one, but the bottom part where the logo is is green, the next section up (the section that contains the Nintendo name) is dark blue. Nintendo Name is green, the 3 color stripes are white-green-white, and the top is dark blue. The zelda logo looks like the logo from Zelda 1, and has link kneeling to the left of it....
On your site, you say you were 5 (-no, not me but the ebay seller-) and didnt remember gettin it, well neither do I. I wsa probably like 5 or 6 too. I didnt know i had it till my mom found it laying in the spare room.... "

And a later email:
"...NOW I REMEMBER WHY I DIDNT REMEMBER GETTING ONE!!!!!! I looked inside the hat.........saw the little tag, and wanted to see what size it was, if it had a size, and there, in faded letters, i saw............my brothers name!! I wasnt mine, but it is now!..."

Full credit for this little real life story goes to:
Chris Fenstermache. Please visit his Nintendo page at http://www.angelfire.com/pa5/nintendoss