Correcting Coordinate Systems in ArcMap

I recently discovered a website that explains how to correct GIS datasets that are in different coordinate systems. If you don't read through the overview, the table of scenarios towards the end includes the most important points. Scenario C seems to apply most frequently to our UP 503 data.

Basically though, open ArcToolbox, browse to Data Management Tools --> Projections and Transformations -->Define Projection. In the Input Dataset or Feature Class field, choose the dataset that doesn't have a defined projection. In the Coordinate System field, click on the icon just to the right of the field. If you use the Import... function, GIS will "match" your dataset with the undefined projections to any dataset you choose.

Also, I found an open source program called MapWindow that includes a plug-in which essentially does the same thing. MapWindow also has some helpful plug-ins for watershed delineations, calculating the area of polygons, and a few other time savers.