I don't have the exact answer, but can throw out some thoughts. It sounds like two things need to be figured out:
1. When looking at all the raster datasets, what is the extent they all have data.
2. Then raster clip to this extent, but without a polygon.
An Idea:
If you have the Spatial Analyst Extension, it may be possible to add the rasters together and come up with a raster that represents the extent of all data. Be careful that when adding rasters that when a No Data pixel and a Data pixel are summed that the Data pixel predominates. This raster addition process could be via Raster Calculator, or by a loop in Modelbuilder or Python. Then use Raster Clip ArcGIS Help (10.2, 10.2.1, and 10.2.2) with the raster you derived as the clipping extent. If you have many rasters, Modelbuilder or Python will come in handy to run through the clipping of all them.
Chris Donohue, GISP