How can I best clean the print bed after a print? I've occasionally had issues with excess filament residue getting stuck to the print bed. There are ways to prevent this, but sometimes even these precautions aren't enough. Over time, residue can build up. I've observed this in some printers, though not others.

Are there any techniques to best clean print beds? In the past, I've used various typical cleaning supplies, with different degrees of success. However, I don't know if this will lead to damage to the printer over time.

The printer I'm using has a glass print bed, which I occasionally partially cover with blue painter's tape during printing.
If you are printing with ABS (or PLA), acetone will dissolve it.  Simply pour
some on the bed and wipe it off (beware, acetone can damage beds that have a coating or a plastic sheet over them, be sure to test this first).

Heating the bed back up may make the plastic softer and easier to
remove.

If you are using tape on the bed, you could remove the tape to remove
the plastic stuck to the tape.