A good place to start would be to consider the attempted suicide of Mildred at the very start of the book in the first chapter. She is clearly punishing herself for the emptiness of her life and the way that she has no purpose or meaning. This results in Montag returning home after a pleasurable day at work to find his wife in bed, barely breathing, with a bottle of sleeping tablets on the floor, which is now empty:
The object he had sent tumbling with his foot now glinted under the edge of his own bed. The small crystal bottle of sleeping tablets which earlier today had been filled with thirty capsules and which now lay uncapped and empty in the light of the tiny flare.
Mildred's act in taking her life (which she seems to have forgotten the next day) seems to be an act of desperation, protesting against the meaninglessness and insignificance of her existence, and punishing herself as a result. If you want other examples, you might want to consider the ambiguous way that Montag often responds to books and the learning that he receives from them.