How do I facilitate keeping multiple grounds, (i.e. AGND, DGND, etc...) separated in the layout when using Eagle?
Create a footprint with GND and AGND pads.  Draw copper between these pads. Yes, this will produce a DRC "Overlap" error as shown below:



This is OK.  There three buttons at the bottom: 


Clear all
Processed
Approve


"Clear all" will temporarily clear the list for this run of the DRC.  I'm not sure why that's useful; just close the window if you want it shortened.

"Processed" will fade out the color of the red X. This is potentially useful if you're iterating through a long list of DRC errors and fixing them as you go; you can keep track of the ones you think you've corrected.

"Approve" is the only one I use on a regular basis.   This moves the error from the errors list to the approved list: 



and keeps it there on subsequent runs of the DRC.  Note that this only moves this specific error with this specific pair of nets at this specific location.  Closing this window and running the DRC again produces the notification "DRC: 1 approved errors"



and no "DRC Errors" dialog.  You can get this dialog back by creating an error, or (preferably) the errors command, the yellow exclamation point in the above screenshot, or the menu Tools -> Errors.

The "Approve" functionality exists for a reason, the same reason that we have tools like 

#pragma GCC diagnostic ignored "-Warning"


Sometimes, it's OK to ignore a DRC error.  This is one of those times.