If, for example, folks started to build BBS-style communities like back in the day where they could communicate and even share files - but now with no long distance charges - that would be really cool.
I have a real C64, but I wouldn't want to run it off of that, since I don't have always-on Internet or power (I travel full-time)...I'd go with an emulator running on a server somewhere. I have my doubts it would actually garner a community, however, which is the primary thing preventing me from putting the effort into it. It'd be fun to tinker, regardless, and I believe Greg Pfountz made Color 64 free software a few years back, so I wouldn't even need to pirate it to obtain it (since I don't have a 1541 or 1571 drive to read the disk, even if it is still readable).
Edit: Color 64 info here http://www.zimmers.net/bbs/c6bbs.html Downloads here: http://software.bbsdocumentary.com/COMMODORE/C64/COLOR64/
I haven't put either online yet even though there are ways out there. But if you got a BBS going, I'd partake in that. There just isn't anything out there. Everyone has moved to forum software these days (and places like HN!).
See my profile here on HN if you ever want to get in touch.
I think most MUDs came about on bigger systems (UNIX systems on campuses, predominantly, but they made their way to PCs) but I seem to recall there were a couple for C64, or at least I know I had friends with C64s that logged into systems that offered MUDs. I never caught the MUD bug, though I did play a number of the games offered on various BBSes.
Anyway, with VICE, one can readily emulate a C64 or C128 with tremendous resources (hard disks, huge RAM disks and expansion, etc.), so I'm certain running a MUD would be possible and reasonably usable, if any exist. In my digging, I found there's a more recent fork of Color 64 called Centipede 128, which is a native 128 application, and can make use of a lot of advanced resources, like hard disks and extended RAM.
While we're shooting the shit about this stuff, I wish more of this development was happening for C128 native. The more I tinker with it, the more annoying it is having such a low res display. Having 80 columns makes it entirely comfortable to use for almost anything, even with my modern 1080p+ habit (hell, I even expect my next phone to have 1080p or better). I use my C64 primarily with MSSIAH for music stuff, and the display is awful. They cram so much on the screen that it's hard to read (but, removing stuff from the screen would make it less useful). A C128 80 column mode would be perfect. Finding programming resources for C128 is also much more difficult. Nonetheless, I'm still looking for a reasonable deal on one. I had a C128D, which I loved, and was a real beast for an 8 bit machine.
But, the 128 80 column mode was entirely usable (it was at 640x200 or 640x400 interlaced, so it was quite legible, and comparable to PC displays of the time). So, I was able to use PC BBSes comfortably from the 128, but not from the 64. I'd be happier, if more software took advantage of the 128. There aren't even any music trackers for the 128, that I can find.
https://en.wikipedia.org/wiki/Contiki#Features
I couldn't find any screenshots of the C64 version of Contiki, but here is the Apple ][ version browsing the web.