This is perhaps the oldest webcam picture of an astronomical object other than the moon. It's dated March 22, 1996.
Ten 2 second exposures were made with a 4-bit greyscale Connectix QuickCam taped to the eyepiece of Celestron 11x80 binoculars (this is one of the original QuickCams, with even more noise and less sensitivity than the second generation greyscale QuickCam).
Any longer than 2 seconds and the room-temperature QuickCam became saturated with noise.
The ten images were stacked and aligned using the layers feature of Photoshop 3.0. I simply adjusted brightness and contrast. No darkframe was subtracted.
As you can see, it actually worked! For posterity, this image was posted to the JPL comet website.
Webcam atrophotography is all the rage among amateur astronomers lately. The manual labor has been reduced by shareware "stacking" programs which can quickly cull and combine hundreds of images.
Patrick Vanouplines has a much more detailed page about photographing Comet Hale-Bopp with a QuickCam a year later.
I did get a chance to visually view Hyakutake from the somewhat dark skies of Petaluma, CA with a large crowd of curious viewers. According to my somewhat-accurate hand measurements, the tail was 35 degrees long! Easily the most impressive comet I have ever seen visually (I missed Ikeya-Seki as a child).
PS: The comet is the fuzzy thing in the middle. The dot at 8 o'clock is a star.