I've got a MICRON Laptop with a 60gb HD and 256mb Ram and whenever I try to install a windows app (like Office or Macromedia Flash) Wine runs but out of the blue WINE freezes up and a windows appears flashing a whole lot of memory info and dump information and exits.:-@ Whats Happening? :-S I've had this happen on RH 7.3, SuSE 9.1 pro and simplyMEPIS 7.

maybe too little ram? what size is swap?
what versions of wine, kde and linux are you using? suse 9.1 is really old
you might consider a minimal distro with a lightweight d.e. with only 256mb , have you tried tinyme? or puppy? or a xfce based distro?

Maybe you should try and update your system? RH 7.3 and SuSE 9.1 aren't really the newest versions of distros. And maybe you should also try to update Wine version (if it's not of the newest version).
I don't really hace any idea, but that'd be the first thing i'd blame and consider updating.
Given that you have quite weak hardware (i guess) then you also might want to try other distros with more optimization facilities, such as Gentoo or even build you own LFS. Again, old software doesn't mean it's better for old hardware.

That would be the Windows application crashing, likely due to a bug in Wine. Which version of wine are you using? If you are using the distro supplied one, then you probably need to upgrade.

I have Wine 1.0.1 and a 150mb Swap. RH 7.3 is 2001 (old) and SuSE 9.1 2004. And MEPIS 7 (2008) is pretty lightweight on my computer. I can't find any packages for puppy related to WINE.

Wine 1.0.1 is fairly recent. You may wish to check their website winehq.org, in particular the compatibility database for more information.