So Word is carbon. Based on this info, one would think that AppleWorks and Word don't support long file names because they're carbon, and you'd think that any Cocoa app would support them, but OmniWeb doesn't. Actually, OmniWeb does something weird: If you save a web page, there's no limit on how long the file name can be, but if it's too long, it comes up with text actually overlapping each other in the download manager, and it doesn't save.
So far, I don't think anything except the Finder supports long file names. Hopefully Apple will support long file names in Cocoa in 10.2.