Ugh, this problem was infuriating. I got a cheap copy of Windows 8 through my job and decided to go ahead and install it, just to be up-to-date. Then, I went to play SSF4AE via Steam and instead of launching, I got an ugly little window that said "An unhandled error has occurred -1."
After digging around online, it appears that the fault lies in Windows 8's default implementation of Games For Windows Live. |:-[
To get around this problem, we need to uninstall the default GFWL and download the latest installer from Microsoft.
You DO NOT have to uninstall/reinstall Steam as is suggested elsewhere online. If you try that, be aware that it
will may uninstall all of your games at the same time (thanks to MasterPhW for the correction). It's supposed to ask before doing so, but it didn't ask me, so YMMV.