This problem is addressed in ArcGIS 8.1 Service Pack 1. See the Related Information section to download this pack.
The Project wizard for shapefiles and geodatabase data in ArcToolbox will display a transformation panel if you are converting between two datums (geographic coordinate systems). No datum transformations are listed even when one or more exists. Two input datasets can have the same coordinate systems. One will work, but the other one won't.
The Project wizard compares the source and target geographic coordinate systems with the list of predefined geographic (datum) transformations. The comparison function is incorrectly checking an internal parameter, LeftLongitude, of the spatial reference. If the LeftLongitude value of the source or target coordinate system differs from the values in the geographic transformations, no transformations are returned.