why does Windows 7 x64 Explorer.exe suddenly gobble up all available RAM and slow my system to a crawl?
Solution 1:
Try running Process Monitor or Process Explorer and capture what happens during "normal" operation as well as during the moments when it seems to slow down. That's a way of troubleshooting it.
You could also try uninstalling Live Mesh and see if it makes a difference.
Solution 2:
Try clearing your thumbnail cache, use disk cleanup to do this.
Also if you have image or especially video files in some of those folders that Windows is unable to generate thumbnails for because it does not have the codec needed, this can cause Explorer issues, slow downs or even crashes.
If you can locate the folders with files that Windows cannot generate a thumbnail for, change the view setting for that folder to something like details, so it will not attempt to generate thumbnails.
If they are MKV video files see this thread