What kind of glue is best for a black plastic kitchen appliance (ABS plastic)?
The surprising (to me) answer may be ABS cement.  You probably won't find this in the hardware store glue isle, instead head over to plumbing:



You'll want the smallest can possible (e.g. 4oz), and after use to seal it in a zipper lock bag and store in a cool dry location.  The stuff goes bad in the can pretty fast.

The ABS cement worked for me far better than any of the other glues mentioned above.  You can also cut out a small piece of ABS drain pipe, or other ABS item, to use as a patch for the repair.

Note that ABS cement is a mix of a solvent and ABS powder: in the end you really end up welding the plastic more than gluing it.  For this reason clamping is recommended.