I'll not forget the first time I sent an email. My cousin had just gone to college and his parents were visiting my parents and I. I somehow got his email address at college, and figured out how to send him an email through a BBS I was using at the time. He was apparently in a computer lab then, because he wrote back within minutes. I called everyone in the house over to see the computer screen. The feeling we all had at seeing a nearly-instant response to a message was just magical, especially since it was "free" (a phone call to him would have incurred long distance charges). I imagine it would be difficult for anyone under the age of about 42-45 to imagine just how mind-blowing this kind of thing was at the time.
I also remember a similar amount of wonderment a few years later seeing a "live" picture over the internet for the first time as you describe - I believe the first one I found was the Netscape Fishcam. Seeing a live picture on a computer from some other part of the country (or world) was just mind boggling.
It all seems routine and even mundane now. I wish I could recapture the sense of excitement the internet had back then.