Infinite Mac is a project by Mihai Parparita to make classic Mac and NeXT emulation easily accessible. It uses WebAssembly ports of Mini vMac, Basilisk II, SheepShaver, DingusPPC, and Previous to allow a broad set of System Software/Mac OS versions to run on the web.
Shortcuts to the most popular versions are available: system6.app, system7.app, kanjitalk7.app, macos8.app, and macos9.app.
The welcome document or Stickies in each machine has instructions. For a demo of the kinds of capabilities the emulators have, see this video.
To learn more, including how it was built, see this series of blog posts. Source code is available on GitHub.
Partly because it evokes Infinite Loop, partly because porting something to the web means it can be run on an almost infinite number of devices, and partly because it's a forever project.
It's a contemporary of classic Mac OS and an ancestor of Mac OS X.
Mac OS X would be great to see, but the primary way to emulate it (QEMU) is currently too slow and complex to be run in a browser. You can subscribe to #72 to get updates if that changes. DingusPPC is a work-in-progress emulator that may eventually be able to run Mac OS X, subscribe to #219 for updates.
The project is focused on classic Macintosh and adjacent systems, but if you're interested in other operating systems, you can check out PCjs or Virtual x86 for Windows, and Apple ][js for ProDOS.
You can reach Mihai via email or @mihaip@hachyderm.io. For bug reports or software requests, you can also file an issue on GitHub.
Using it, sharing it, and giving feedback is the best way. If you'd like to support the project financially, you can donate.