I have been using Windows Millennium (OEM version) extensively on all sorts of PCs, it hasn't BSOD'd once. It's the same thing as 98SE, but with added features and improvements. I LOVE the built-in USB mass storage drivers, that's a life saver when the motherboard is too new for 98SE or Millennium.
Maybe it's the Retail or Upgrade versions of Windows Me, but the OEM version works perfectly fine.
In all my 9x experience, they all have the same odds of getting the BSOD. If you get it, then it means you did something very wrong, like installing a bad driver or fucking with the system files. If you behave, 9x will behave.
The nice thing with Windows ME is it includes System File Protection and System Restore.