Hi Anne,
A couple of things occurred to me.
Did you move any shapefiles recently? If so, possibly the .prj file was missed (I think this possibility is unlikely).
Instead, I think one or more layers is missing its coordinate system or has a wrong coordinate system. For one that was missing, you had the map (data frame) using the same coordinate system so it didn't matter. That is, the "unknown" data wasn't being projected on-the-fly. If the data frame's coordinate system was changed, then the layer wouldn't line up anymore.
Add some data that you know is correct to the map and compare the other data with it. That should confirm which layers have missing or incorrect coordinate systems (because they won't line up).
If you want, you can post the data extents + current coordinate system, and a general idea of where the data should be in decimal degrees, or county/city/etc. Someone may be able to figure out what's going on.
Melita