there were many ways to use the internet before browsers, applications talked with other applications, people joined BBSs, but you could argue that eventually, you'd like to access text or media in a repeatable manner, you'd like to be able to point to those resources in the least steps possible (some way of universally locate a resource...), those resources will end up being referenced by other resources and you'd eventually end up with the web.

the web is a side-effect of the internet

I was using the Internet before the WWW, and there was already a pretty good ecosystem from nerdy stuff to consumer-usable. Email, Usenet, Gopher, FTP, IRC, were all widely usable.

Gopher especially made a great way to index and search (with WAIS) things on multiple different services, without being a mess of text/hyperlinks/images/sound/video in a hairy ball like the WWW.

Gopher

One of the things no one has talked about here are consumer content delivery services like AOL and Prodigy. These created some of the first Internet walled gardens, with programs created to serve these services' content via phone lines. As consumers moved to broadband, I would expect these programs to become free and be the primary way for consumers to view content.

Browsers made the Internet usable for the general population. The Internet as we know it would have remained a network for academia, governments and large corporations. Smartphones would not have been developed. Without a reason for everyone's homes to be connected to a high speed network, TV would remain the remit of cable and satellite broadcasting - no streaming services.

We'd have something similar. Maybe more fragmented like Usenet + telnet BBSes + gopher + IRC, or a closed standard like hypercard that you had to license. People want to communicate and put stuff out there to be heard, it'd have happened somehow.

NNTP FTW. There was nothing more entertaining than Usenet. I loved it, really.