Ok, I am having no luck in following what y'all have done. I have the same task, multiple (100+) rasters of different extents and most not overlapping (But in the same area) that I am simply trying to sum the values (0,1). The map is going to show how many times a given cell was "treated". All the rasters have had the noData changed to 0 (Using the reclassify tool, a lot easier than raster math).
So I tried to do the cell statistics. The first attempt started with the creation of a basemap of pixel values of 0, which covers all the other cell locations. I then entered a subset of maps (for the one year) that included the basemap. I set it to run "sum". I then set the environment settings as mattlove described (set spatial, snap raster, raster analysis settings to the basemap and chose untion of inputs). But I still get "Invalid Output Extent". When I set the Processing Extent to the basemap, it runs but the output is blank/corrupted/I have no idea why there's no data.
What've done, just so I can get this rolling while someone else can help me figure out whats going wrong, is mosaic the pieces to the basemap (Using Mosaic to Net Raster). Then I can use the Cell Statistics tool to sum all the maps now that they are all the same size. This process is not time efficent at all, I've tried building a model to run this but that hasn't worked out yet.
Please tell me ESRI has created a tool that does this or help me figure out what I'm doing wrong with Cell Statistics that it won't cooperate.