The origin of the very first sticker is not and probably will never be known. The creator of the Calvin and Hobbes comic Bill Watterson was never into mass marketing, and therefore never produced actual "Calvin and Hobbes" merchandise (not counting the comics/books of course). This is why every Calvin & Hobbes t-shirt you see isn't a "genuine product" and is not endorsed in any legal manner. Read: They are infringing on a copyright and are technically illegal. So are the stickers which use the character's likeness. This is typically why the producers of these products tend to remain anonymous, and is also why we will probably never really know who started this whole thing.
If memory serves me I first saw one that had 'Calvin' pissing on a Ford or Chevy logo, however there really wasn't a copyright on the sticker so their was no way of telling this was authentic. But I first saw these things in like 95' in the summer. So that's when I think they started appearing. But due to his popularity in the early 90's the image was so well known that every one knew the rambunctious brat known as Calvin. Known for his intelligent arguments and obnoxious faces the stickers would have been a great success from the start. But yeah there annoying but the first amendment protects there freedom to show the world how they feel and I kinda get a chuckle out of them once in a while.
I designed one for a Interpersonal communications class at the University of Maine at Orono in 1992. I had designed Clavin peeing on the Black Bears heads, with the words "I'm Outta Here!" since I was graduating. One of my classmates asked if he could keep the art work. I let him since it was just a doodle. Then when I started to see them on car windows, I had to wonder if he used them. I thought he was a business major...