We are still using ArcIMS with shapefiles - pulling the software down each night and copying shapefiles across at the file level has worked well for us for (many) years.
However we are trying to migrate to ArcGIS for Server, and that doesn't seem to perform too well with shapefiles, so we are also migrating to using file geodatabases as our default storage format - hence this thread.
Versioned editing would not be appropriate because we do not hold most of our data in SDE - we've only found that useful for large fairly static datasets, such as aerial imagery and basemapping. Until recently shapefiles easily out performed SDE for small datasets. I've briefly looked at distributed geodatabases and it might be an option, but I think that's probably overcomplicated for the type of data we are looking at.
I'm interested that you say you don't always have to stop the services - I've been playing on our test servers and I can overwrite a *.gdb folder in Windows Explorer when the data is in use and ArcGIS for Server picks the changes up straight away. However I can't delete a *.gdb folder that is in use. Uisng Catalog I can rename a feature class within a fgdb and copy the new one in, but Server does not pick up the new data until the map service is restarted.
Cheers,
Sarah.