The result is often a classic game running on a modern system without needing to jump through hoops, which is a huge win to people who enjoy playing the game in question.
OpenTTD, OpenRCT2, and OpenMW all come to mind, not to mention the many ports of Id games.
They are reimplementations but sadly far from clean room. The ASM was often referenced and even used side by side as the projects migrated to their own code base.
That should be feasible even with emulation. My memory seems to be a bit faulty, but IIRC UltraHLE could run SM64 at full speed on systems with less than 1GB and 1Ghz.
I can't remember if it was full speed but it was perfectly playable to emulate SM64 with UltraHLE on my Pentium 200MMX OC to 225MHz with a Voodoo 2 8MB and 96MB of RAM.
I had to run it in Windows NT5 beta though, it stuttered in Windows 95.
OpenTTD, OpenRCT2, and OpenMW all come to mind, not to mention the many ports of Id games.