The Ex-wife of Smithers is the ex-wife of Waylon Smithers. She had a very brief appearance in the episode "Secrets of a Successful Marriage", where she appears in a flashback where it is said that Smithers was briefly married to her, but they divorced because he devoted a lot of time to Mr. Burns, whom she disliked because of his generally cold-hearted and often selfish personality, notably towards her husband. In one particular instance that Smithers indicated led to their separation, she asked what was troubling her husband (who had an unspecified leg injury that required him to use a cast and crutches), and asked if it had anything to do with Mr. Burns and described him as awful, which caused Smithers to explode at her and demand she leave him out of it before smashing several liquor bottles before Mr. Burns was heard calling for Smithers, to the latter's evident delight.
It is possible that Smithers would leave her to be with Mr. Burns, or that she was the one who abandoned him because he dedicated a lot of time to Mr. Burns. Based on her accent when speaking, she presumably hailed from the Southern region of the United States.
Behind the Laughter
Smithers' ex-wife was going to be mentioned in Blood Feud where Smithers, in response to Burns' ailing health and the possibility of him dying, requested that the latter let him have "enough so he can go back to his wife and kids", implying that during their marriage she and Smithers sired at least two children. However, the line ended up cut due to time constraints.
She eventually appeared in Secrets of a Successful Marriage in a flashback for Smithers explaining how they separated. The scene itself was taken directly from two plays by the playwright Tennessee Williams: Cat on a Hot Tin Roof and A Streetcar Named Desire.