I remember first seeing Mosaic when I started taking classes at Brown University. The university CS department people had very wisely set it up so that any CS students could not only very easily create their own Web pages from files in their home directory, but also easily do CGI scripts that were publicly accessible. The easy CGI wasn't so great for security, but was fabulous for lowering the barrier to experimenting.
Using that CGI, I wrote several services, mostly in Perl, and one in C. (The C one was so that I could use the GD library to draw some GIF parts of a hypermedia image of the main workstation lab, with faces of people there, which machines were free, etc., since it wasn't doable as well in HTML at the time.)
After seeing it at the university, I also went and and installed Mosaic and a the NCSA or Apache HTTP server at my workplace (where I was in an R&D group), and wrote some demonstrations of it (e.g., doing our engineering documents in it instead of Interleaf/FrameMaker, clickable hypermedia floorplan).
I'd actually already been on the Internet as a kid (gateways, email, Usenet, ftp, etc.), and had already worked with a few offline hypertext systems before I saw the Web (as well as being aware of earlier grand visions), but the Web was obviously going to let us do Internet things we couldn't before, and also accelerate bringing the goodness of the Internet to everyone. (Well, we dropped the ball on some of the goodness, but it still happens, just not as much nor nearly as universally as we'd hoped, and we can still improve that.)