According to WinMX, the system requirements are:

Windows 95/98/ME/NT/2000
Internet Explorer 4.0 or above if running Win95/NT
Pentium 166 w/ 64MB ram or better recommended

However, I've successfully run WinMX on a far less powerful PC. WinMX is more resource-intensive than some comparable programs, but if you can devote your PC primarily to sharing, here's what I consider the minimum requirement:

Windows 95/98/ME/NT/2000
Internet Explorer 4.0 or above if running Win95/NT
Pentium 75 w/ 24MB RAM

In fact, I was able to run so many apps at once that I'm pretty sure WinMX will run just fine in a P75 with only 16M of RAM.

My P75 was able to simultaneously send and receive at my modem connection's full capacity (~3 Kbps outbound, ~ 5.5 Kbps incoming [concurrently, once I'd applied the bandwidth throttle]) even while playing MP3s in Winamp. I should point out however that my sharing box has a "real" (hardware) modem, not one of those cheap "win" (software) modems, which leech off the cpu. It could even do other stuff at the same time, but the machine was clearly nearing its limits, and the screen updates (hotlist, transfers) were becoming visibly/annoyingly slow, even though the transfers were still moving right along.

I've since upgraded my sharing box to a P120 with 32M RAM, and now it has some oomph to spare.

By the way, you don't need to actually run MSIE, you only need to have it (I think WinMX uses part of it just to display 2 small graphic images.)

So I don't think you should let ownership of a sub-166 MHz PC keep you from trying -- and using -- WinMX.