I do remember the Internet before the web. We used gopher, ftp, irc, telnet, archie, veronica and a whole lot of other services whose function is now better served by websites. (With the exception of telnet, which thankfully has been replaced by SSH).
I remember before Internet was widespread, the question of "who is that guy that was in that movie with that girl and the theme song that went dun-dun-doo-dun was" was not something you necessarily ever expected to find the answer to in your lifetime.
Files exceeding a megabyte in size were huge. Even during the early days of the web, images took long enough to download that we would put low-res placeholders in our web pages. E-mail signatures were ideally limited to four lines of text. HTML email was the thing of noobs with no regard for storage space.
Streaming video was crazytalk. I mean do you have any idea how long it takes to transfer an entire video disc worth of data over a 64kbps link anyway?
My entire college was on a 64kbps link at the time. We noted a significant speed increase when they switched to a blazing 256kbps later. I now have 10 Mbps--40 times more--for my personal use.
Yeah, I remember. #feelingold