We shared (some) savegames, custom levels/tracks, and high scores on 3.5" disks, so I’ll stick to “always.” 
The main difference in my case is that I’ve had two or three computers just for me for “only” a little over a decade, so it’s become pertinent to be able to switch over from playing at my desktop to lying down on the couch (or whatever) since then, at least if the game runs well on both systems.
I’ve been using Dropbox for (some) ScummVM saves since 2010 (?), for example, and Unison in a much more limited form (as far as savegames go) probably since '07 when I built my first/third desktop.
In fact I probably did very little savegame sharing at all except for ScummVM, which ran equally well on all three of my systems. That’s desktop, proper laptop, and netbook. The latter two have been subsumed by my current thin, light laptop that’s roughly on par with my proper '09 laptop as far as most performance goes, except it’s much much lighter and the battery lasts longer.
But there is, sort of. ScummVM is about as user-friendly as they come as far as sticking in your own save path goes, but I’ve never had a thought along the lines of “oh, how convenient!” or “what a nice surprise!” like I experienced with Escape from Monkey Island on GOG Galaxy yesterday.
It’s never bothered me sufficiently to look into it or anything, and heck, that very well may not even change. But after the graphical glitches disappointment mentioned above, it was a nice surprise.