Probably not. This DCOM exploit is not known to affect Win9x (including WinME.) It is known to affect any version of Windows using the NT Kernel. This includes WinNT 3.51, 4.0 Workstation and Server, Win2K (all versions), WinXP and Win2003.
Unfortunately, Windows NT 3.51, and Windows 4.0 Workstation are no longer supported by Microsoft and no patch has, or will be, issued for those products.
In fact, while both of these products have been proven by outside agencies to be infectible, Microsoft has not seen fit to recognize that fact in their security bulletins.
There have been some rumors that running Win9x with the Microsoft Personal Web Server can make your computer vulnerable to this exploit. There is no significant data to suggest that this is, in fact, the case.
To be entirely safe you can install a personal firewall that blocks TCP and UDP ports 135, 137, 138, 445 and 4444 or you can get out your wallet and buy a supported copy of Windows.
Needless to say, the "mainstream" news media has been universally reporting that the exploit affects "essentially all versions of Windows."
Aren't something like 30% of PC owners still running Win98? This sort of piss-poor journalism can cause these people a lot of grief as they run around looking for patches to their systems that are not needed and, indeed, do not exist.
By all means. Get the latest windows and still find yourself being hacked.
Or, next time your PC needs to be reloaded, (Which should be NOW btw, if you got infected, because there is no way to tell how much damage was done.) Why not download a copy of RedHat, Mandrake, Debian, or SUSE Linux and install it instead of windows. Use it for a few days to a week. If you find it doesn't suit the way you like to work with a computer, you can always simply reload windows, and you're no worse off than you were before, but you will at least have tried to get off the windows treadmill.