Converting Geodatabases to Shapefiles and Reprojecting Data in ArcGIS

1. Open an empty Arcmap and open the Geodatabase containing the layers you wish to convert/reproject.
2. Go to the View Menu and choose Data Frame Properties . . .
3. In the Data Frame Properties Dialog Box choose the Coordinate System tab. The current coordinate system that appears should be the same as that of the Geodatabase (likely Tennessee State Plane if you're using TDEC data). We're going to change the coordinate system for the data frame to whatever the new coordinate system you want to use for your exported data.
4. Change the coordinate system for the data frame. If you're converting from TN State Plane to Decimal Degrees, choose the following in the "Select a Coordinate System" box: Expand "Predefined", Expand "Geographic Coordinate Systems", Expand "North America", Select "North American Datum 1983". Click Apply and OK, and then Yes to the warning dialogs if they appear. (The warnings shouldn't apply to the data we use unless you've got something in the older North American Datum 1927. A lot of decimal degrees data is in the WGS 1984 datum which is just a worldwide expansion of NAD 1983.)
5. To Export as a shapefile in decimal degrees, you simply left-click on each feature layer in the geodatabase and choose Export . . . Make sure that you click the "Use the same coordinate system as: the data frame" radio button--this will apply the coordinate system you just set to the shapefiles you output:

You're done! If necessary you may with to go into your View-->Data Frame Properties and change your coordinate system settings back to the original coordinate system. For Tennessee State Plane (TDEC's standard), you'd choose Predefined-->Projected Coordinate Systems-->State Plane-->NAD 1983(Feet)-->NAD 1983 StatePlane Tennessee FIPS 4100 (Feet).