The big obvious one is web-based tooling. Your information & settings are stored on a server and you use a web browser to view it via whatever device you're on. For more locally based workflows, we have networked filesystem protocols, automatic syncing between systems, that kind of thing. It's not a 1-1 equivalent of running a remote program and viewing it locally obviously, but it gets the same job done, in a much more useful & flexible manner than X forwarding did.

For example, the remote mail client usecase I was replying to is simply done with a webmail client today.

IIRC, it's not that secure though.. I'm really surprised people didn't do more things like send animated skulls to people's desktops.